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Trigonometry is a branch of mathematics that studies triangles and the relationships between the lengths of their sides and the angles between those sides. It defines trigonometric functions that describe these relationships and are applicable to cyclical phenomena like waves. Trigonometry has its origins in ancient Greek and Indian mathematics and was further developed by Islamic mathematicians. It is the foundation of surveying and has many applications in fields like astronomy, music, acoustics, and more.

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Trigonometry101

Lecture Presentation on Trigonometry, types of angle, angle measurement, pythagorean theorem, trigonometric function, trigonometric relationship, circle function, co function, reference angle, odd even function,graphing of trigonometric function, special angles and terminology and history of trigonometry

Trigonometry

This document discusses trigonometric ratios and functions. It defines the sine, cosine, and tangent ratios for right triangles. It also introduces the reciprocal functions of cosecant, secant, and cotangent. Special angle values for trig functions are provided in a table. The document explains how to write trig functions in terms of x, y, and r using the Cartesian plane and use a CAST diagram to determine the quadrants where trig ratios are positive and negative. Finally, it discusses extending knowledge of special angles using trig ratio definitions in the Cartesian plane.

History Of Mathematics

All about how Number s were developed, Geometry, Arithematic Operations. DO NOT UNDER ESTIMATE WITH THE FRIEND COVER.

Trigonometry

This document provides an overview of trigonometry presented by Vijay. It begins by listing the materials needed and encouraging note taking. The presentation then defines trigonometric ratios like sine, cosine and tangent using a right triangle. It also covers trigonometric ratios of specific angles like 45 and 30 degrees as well as complementary angles. The document concludes by explaining several trigonometric identities and providing a short summary of key points.

Maths in origami

The document discusses the use of mathematics in origami. It begins with a brief history of origami and definitions of key terms. It then explains Maekawa's theorem, which states that for any vertex in an origami crease pattern, the number of mountain creases minus the number of valley creases must equal 2. The document provides a proof of this theorem by showing how flat origami can be folded to form polygons, and relating the interior angles to mountain and valley creases. Finally, it discusses how origami can be used to modularly construct polyhedra through techniques like Sonobe units.

Trigonometry

Trigonometry deals with relationships between sides and angles of triangles, especially right triangles. It has many applications in fields like architecture, astronomy, engineering, and more. The document provides background on trigonometry, defines trigonometric functions and ratios, discusses right triangles, and gives several examples of how trigonometry is used in areas like navigation, construction, and digital imaging.

History of trigonometry clasical - animated

Trigonometry
History of Trigonometry
Principles of Trigonometry
Classical Trigonometry
Modern Trigonometry
Trigonometry
History of Trigonometry
Principles of Trigonometry
Classical Trigonometry
Modern Trigonometry
Trigonometric Functions

Introduction To Trigonometry

It is a ppt on Trigonometry for th students of class 10 .
The basic concepts of trigonometry are provided here with examples Hope that that you like it .!! Thankyou ..!! :)

Trigonometry101

Lecture Presentation on Trigonometry, types of angle, angle measurement, pythagorean theorem, trigonometric function, trigonometric relationship, circle function, co function, reference angle, odd even function,graphing of trigonometric function, special angles and terminology and history of trigonometry

Trigonometry

This document discusses trigonometric ratios and functions. It defines the sine, cosine, and tangent ratios for right triangles. It also introduces the reciprocal functions of cosecant, secant, and cotangent. Special angle values for trig functions are provided in a table. The document explains how to write trig functions in terms of x, y, and r using the Cartesian plane and use a CAST diagram to determine the quadrants where trig ratios are positive and negative. Finally, it discusses extending knowledge of special angles using trig ratio definitions in the Cartesian plane.

History Of Mathematics

All about how Number s were developed, Geometry, Arithematic Operations. DO NOT UNDER ESTIMATE WITH THE FRIEND COVER.

Trigonometry

This document provides an overview of trigonometry presented by Vijay. It begins by listing the materials needed and encouraging note taking. The presentation then defines trigonometric ratios like sine, cosine and tangent using a right triangle. It also covers trigonometric ratios of specific angles like 45 and 30 degrees as well as complementary angles. The document concludes by explaining several trigonometric identities and providing a short summary of key points.

Maths in origami

The document discusses the use of mathematics in origami. It begins with a brief history of origami and definitions of key terms. It then explains Maekawa's theorem, which states that for any vertex in an origami crease pattern, the number of mountain creases minus the number of valley creases must equal 2. The document provides a proof of this theorem by showing how flat origami can be folded to form polygons, and relating the interior angles to mountain and valley creases. Finally, it discusses how origami can be used to modularly construct polyhedra through techniques like Sonobe units.

Trigonometry

Trigonometry deals with relationships between sides and angles of triangles, especially right triangles. It has many applications in fields like architecture, astronomy, engineering, and more. The document provides background on trigonometry, defines trigonometric functions and ratios, discusses right triangles, and gives several examples of how trigonometry is used in areas like navigation, construction, and digital imaging.

History of trigonometry clasical - animated

Trigonometry
History of Trigonometry
Principles of Trigonometry
Classical Trigonometry
Modern Trigonometry
Trigonometry
History of Trigonometry
Principles of Trigonometry
Classical Trigonometry
Modern Trigonometry
Trigonometric Functions

Introduction To Trigonometry

It is a ppt on Trigonometry for th students of class 10 .
The basic concepts of trigonometry are provided here with examples Hope that that you like it .!! Thankyou ..!! :)

Trigonometric Ratios of Special Angles.pptx

This document discusses trigonometric ratios in right triangles. It explains that there are six trigonometric ratios that can be derived using the opposite, adjacent, and hypotenuse sides of a right triangle in relation to the reference angle. These six ratios are: sine, cosine, tangent, cosecant, secant, and cotangent. It defines each ratio and notes that the opposite and adjacent sides can be interchangeable depending on where the reference angle is located. The document encourages the reader to remember these concepts and concludes with a quote about life being like math.

History of trigonometry2

Trigonometry developed from studying right triangles in ancient Egypt and Babylon, with early work done by Hipparchus and Ptolemy. It was further advanced by Indian, Islamic, and Chinese mathematicians. Key developments include Madhava's sine table, al-Khwarizmi's sine and cosine tables, and Shen Kuo and Guo Shoujing's work in spherical trigonometry. European mathematicians like Regiomontanus, Rheticus, and Euler established trigonometry as a distinct field and defined functions analytically. Trigonometry is now used in many areas beyond triangle calculations.

3 d shapes

This document defines and provides examples of polyhedrons, which are 3D shapes with polygon faces. It lists common polyhedrons like cubes, cuboids, spheres, cones, and cylinders. It provides the key definitions of vertices, faces, and edges. Examples are given for cubes, cuboids, pyramids, cylinders, and cones showing their number of faces, edges, and vertices. Nets for representing the shapes of cubes, cuboids, pyramids, cylinders, and cones are also described.

Trigonometry

Trigonometry is the study of relationships between the sides and angles of triangles. It has its origins over 4000 years ago in ancient Egypt, Mesopotamia, and the Indus Valley. The first recorded use was by the Greek mathematician Hipparchus around 150 BC. Trigonometry defines trigonometric functions like sine, cosine, and tangent that relate angles and sides of a triangle. It has many applications in fields like astronomy, navigation, engineering, and more.

Transformation Geometry

This document discusses translations in geometry. It begins by defining a translation as a horizontal or vertical slide that moves a figure without changing its shape or size. It then provides examples of translating points and figures by:
1) Translating individual points on a coordinate plane by moving them horizontally and vertically.
2) Translating triangles by moving their vertices horizontally and vertically, which demonstrates the triangle retains its shape and size.
3) Describing translations algebraically using notation like (x+p; y+q) to indicate a figure is translated p units horizontally and q units vertically.

medieval European mathematics

The document discusses medieval mathematics from the 12th-14th centuries. It provides biographies of several important medieval mathematicians including Fibonacci, who introduced the Fibonacci sequence to Western Europe and studied rabbit populations. It also discusses Nicole Oresme who proved the divergence of the harmonic series and Giovanni di Casali who analyzed accelerated motion graphically. The document notes that during this time, Europeans learned mathematics from Arabic sources that had been translated to Latin.

The Egyptian Rope Stretchers

The ancient Egyptians used ropes with evenly spaced knots to help measure right triangles and establish property boundaries. Scribes and their assistants would hold the ropes at specific knots to form a right triangle, demonstrating their understanding of the Pythagorean theorem. While the Egyptians did not name the theorem as such, there is evidence they knew and utilized the relationship between the sides of a right triangle, potentially informing Pythagoras' later work developing this mathematical concept.

Heron’s formula

I can say this power point will help you to know about "HERON’S FORMULA". You will understand the meaning of 'HERON’S FORMULA'.This power point is best for class 9.
Monish Jeswani.
Thank You!!!!

history of trigonometry

Trigonometry is the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six trigonometric functions - sine, cosine, tangent, cotangent, secant, and cosecant. Trigonometry originated in ancient civilizations for practical geometry applications and was further developed by Greek mathematicians like Hipparchus and Ptolemy. Indian and later Islamic mathematicians made important contributions, including the first tables of sines and tangents. Trigonometry was an important tool for astronomy and passed to Europe during the Middle Ages, with major works by Menelaus and Regiomontanus.

Ancient math

The document summarizes the early mathematical system developed by the Sumerians in Mesopotamia between the Tigris and Euphrates Rivers. Key points:
- The Sumerians developed one of the earliest known writing systems, cuneiform script, which enabled recording of early mathematics on clay tablets.
- They used a sexagesimal (base-60) numeric system combined with a place-value notation, which was superior to later Greek and Roman systems for calculating fractions and powers.
- Much of what is known about early Mesopotamian mathematics comes from clay tablets dating to the Old Babylonian period from around 1800-1600 BCE. These included table texts and problem texts.

Introduction to trignometry

INTRODUCTION TO TRIGNOMETRY OF CLASS 10. IT ALSO INCLUDES ALL TOPIC OF TRIGNOMETRY OF CLASS 10 WITH PHOTOS AND DERIVATIOM

Surface ARea of Prisms and Cylinders

This document discusses finding the surface area of prisms and cylinders. It provides formulas for calculating surface area of rectangular prisms as S = 2lw + 2lh + 2wh and cylinders as S = 2πr^2 + 2πrh. Examples are given of finding surface areas of various prisms and cylinders using their nets. The document ends with a lesson quiz asking the reader to find surface areas of given figures.

Symmetry

Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement")[1] in everyday language refers to a sense of harmonious and beautiful proportion and balance.[2][3][a] In mathematics, "symmetry" has a more precise definition, that an object is invariant to any of various transformations; including reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart, they are related, so they are here discussed together.
Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, theoretic models, language, music and even knowledge itself.[4][b]
This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and nature; and in the arts, covering architecture, art and music.
The opposite of symmetry is asymmetry.
In geometry[edit]
Main article: Symmetry (geometry)
The triskelion has 3-fold rotational symmetry.
A geometric shape or object is symmetric if it can be divided into two or more identical pieces that are arranged in an organized fashion.[5] This means that an object is symmetric if there is a transformation that moves individual pieces of the object but doesn't change the overall shape. The type of symmetry is determined by the way the pieces are organized, or by the type of transformation:
An object has reflectional symmetry (line or mirror symmetry) if there is a line going through it which divides it into two pieces which are mirror images of each other.[6]
An object has rotational symmetry if the object can be rotated about a fixed point without changing the overall shape.[7]
An object has translational symmetry if it can be translated without changing its overall shape.[8]
An object has helical symmetry if it can be simultaneously translated and rotated in three-dimensional space along a line known as a screw axis.[9]
An object has scale symmetry if it does not change shape when it is expanded or contracted.[10] Fractals also exhibit a form of scale symmetry, where small portions of the fractal are similar in shape to large portions.[11]

Trigonometry

Kartikeya Pandey thanks his teacher Ms. Meha Bhargava and principal Ms. Jasleen Kaur for allowing him to complete a project on trigonometry. He also thanks his parents and friends for their help. The document then provides information on trigonometry including its origins in ancient mathematics, definitions of key terms like sine, cosine, and tangent. It also discusses right triangles, angle measurement in degrees and radians, trigonometric functions, trigonometric identities, and applications of trigonometry.

Triangles

Triangles are three-sided polygons that have three angles and three sides. There are three main types of triangles based on side lengths: equilateral (all sides equal), isosceles (two sides equal), and scalene (no sides equal). The interior angles of any triangle always sum to 180 degrees. Important triangle properties include the exterior angle theorem, Pythagorean theorem, and congruency criteria like SSS, SAS, ASA. Common secondary parts are the median, altitude, angle bisector, and perpendicular bisector. The area of triangles can be found using Heron's formula or other formulas based on side lengths and types of triangles.

Pythagorean Theorem

Pythagoras was an ancient Greek thinker, but he was not the founder of the Pythagorean theorem. That honor goes to his followers, known as the Pythagorean Brotherhood, who established the theorem over 100 years after Pythagoras' death. The Pythagorean theorem states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This relationship has many practical applications in fields like engineering, construction, physics, and astronomy that involve calculating distances.

Ppt on trignometry by damini

This project on trigonometry was designed by two 10th grade students to introduce various topics in trigonometry. It includes sections on the introduction and definition of trigonometry, trigonometric ratios and their names in a right triangle, examples of applying ratios to find unknown sides, reciprocal identities of ratios, types of problems involving calculating ratios and evaluating expressions, value tables for common angles, formulas relating ratios, and main trigonometric identities. The project was created under the guidance of the students' mathematics teacher.

Introduction to trigonometry

This document discusses trigonometric ratios and identities. It defines trigonometric ratios as relationships between sides and angles of a right triangle. Specific ratios are defined for angles of 0, 30, 45, 60, and 90 degrees. Complementary angle identities are examined, showing ratios are equal for complementary angles (e.g. sin(90-A)=cos(A)). Trigonometric identities are derived from the Pythagorean theorem, including cos^2(A) + sin^2(A) = 1, sec^2(A) = 1 + tan^2(A), and cot^2(A) + 1 = cosec^2(A). Examples are provided to demonstrate using identities when

Tests of divisibility

This document provides simple tests and tricks for determining if a number is divisible by certain integers between 2 and 11. It explains that to check divisibility by:
- 2, look at the last digit
- 3, sum the digits and check if divisible by 3
- 4, check if the last two digits are divisible by 4
- 5, check if the last digit is 0 or 5
- 6, check if divisible by both 2 and 3
- 8, check if the last three digits are divisible by 8
- 9, sum the digits and check if divisible by 9
- 10, check if it ends in 0
- 11, take the difference of sums of odd and even place digits.

Trigonometry Exploration

This document summarizes a student project on trigonometry. It was created by a class of 10 students along with their math teacher to help students learn trigonometry through practical experiments and research. The project covers the basics of trigonometry including definitions, history, applications like measuring inaccessible heights, and examples of using trigonometric functions and identities to solve problems.

Trigonometry

Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. It emerged from applications of geometry to astronomy in the 3rd century BC. Trigonometric functions relate ratios of sides of right triangles to angles and allow for determination of all angles and sides from just one angle and one side. Trigonometry is used in many fields including astronomy, navigation, music, acoustics, optics, engineering, and more due to applications of triangulation and modeling periodic functions.

Trigonometry

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles in triangles. The key concepts are the trigonometric functions sine, cosine, and tangent, which describe ratios of sides of a right triangle. Trigonometry has applications in fields like navigation, music, engineering, and more. It has evolved significantly from its origins in ancient Greece and India, with modern definitions extending it to all real and complex number arguments.

Trigonometric Ratios of Special Angles.pptx

This document discusses trigonometric ratios in right triangles. It explains that there are six trigonometric ratios that can be derived using the opposite, adjacent, and hypotenuse sides of a right triangle in relation to the reference angle. These six ratios are: sine, cosine, tangent, cosecant, secant, and cotangent. It defines each ratio and notes that the opposite and adjacent sides can be interchangeable depending on where the reference angle is located. The document encourages the reader to remember these concepts and concludes with a quote about life being like math.

History of trigonometry2

Trigonometry developed from studying right triangles in ancient Egypt and Babylon, with early work done by Hipparchus and Ptolemy. It was further advanced by Indian, Islamic, and Chinese mathematicians. Key developments include Madhava's sine table, al-Khwarizmi's sine and cosine tables, and Shen Kuo and Guo Shoujing's work in spherical trigonometry. European mathematicians like Regiomontanus, Rheticus, and Euler established trigonometry as a distinct field and defined functions analytically. Trigonometry is now used in many areas beyond triangle calculations.

3 d shapes

This document defines and provides examples of polyhedrons, which are 3D shapes with polygon faces. It lists common polyhedrons like cubes, cuboids, spheres, cones, and cylinders. It provides the key definitions of vertices, faces, and edges. Examples are given for cubes, cuboids, pyramids, cylinders, and cones showing their number of faces, edges, and vertices. Nets for representing the shapes of cubes, cuboids, pyramids, cylinders, and cones are also described.

Trigonometry

Trigonometry is the study of relationships between the sides and angles of triangles. It has its origins over 4000 years ago in ancient Egypt, Mesopotamia, and the Indus Valley. The first recorded use was by the Greek mathematician Hipparchus around 150 BC. Trigonometry defines trigonometric functions like sine, cosine, and tangent that relate angles and sides of a triangle. It has many applications in fields like astronomy, navigation, engineering, and more.

Transformation Geometry

This document discusses translations in geometry. It begins by defining a translation as a horizontal or vertical slide that moves a figure without changing its shape or size. It then provides examples of translating points and figures by:
1) Translating individual points on a coordinate plane by moving them horizontally and vertically.
2) Translating triangles by moving their vertices horizontally and vertically, which demonstrates the triangle retains its shape and size.
3) Describing translations algebraically using notation like (x+p; y+q) to indicate a figure is translated p units horizontally and q units vertically.

medieval European mathematics

The document discusses medieval mathematics from the 12th-14th centuries. It provides biographies of several important medieval mathematicians including Fibonacci, who introduced the Fibonacci sequence to Western Europe and studied rabbit populations. It also discusses Nicole Oresme who proved the divergence of the harmonic series and Giovanni di Casali who analyzed accelerated motion graphically. The document notes that during this time, Europeans learned mathematics from Arabic sources that had been translated to Latin.

The Egyptian Rope Stretchers

The ancient Egyptians used ropes with evenly spaced knots to help measure right triangles and establish property boundaries. Scribes and their assistants would hold the ropes at specific knots to form a right triangle, demonstrating their understanding of the Pythagorean theorem. While the Egyptians did not name the theorem as such, there is evidence they knew and utilized the relationship between the sides of a right triangle, potentially informing Pythagoras' later work developing this mathematical concept.

Heron’s formula

I can say this power point will help you to know about "HERON’S FORMULA". You will understand the meaning of 'HERON’S FORMULA'.This power point is best for class 9.
Monish Jeswani.
Thank You!!!!

history of trigonometry

Trigonometry is the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six trigonometric functions - sine, cosine, tangent, cotangent, secant, and cosecant. Trigonometry originated in ancient civilizations for practical geometry applications and was further developed by Greek mathematicians like Hipparchus and Ptolemy. Indian and later Islamic mathematicians made important contributions, including the first tables of sines and tangents. Trigonometry was an important tool for astronomy and passed to Europe during the Middle Ages, with major works by Menelaus and Regiomontanus.

Ancient math

The document summarizes the early mathematical system developed by the Sumerians in Mesopotamia between the Tigris and Euphrates Rivers. Key points:
- The Sumerians developed one of the earliest known writing systems, cuneiform script, which enabled recording of early mathematics on clay tablets.
- They used a sexagesimal (base-60) numeric system combined with a place-value notation, which was superior to later Greek and Roman systems for calculating fractions and powers.
- Much of what is known about early Mesopotamian mathematics comes from clay tablets dating to the Old Babylonian period from around 1800-1600 BCE. These included table texts and problem texts.

Introduction to trignometry

INTRODUCTION TO TRIGNOMETRY OF CLASS 10. IT ALSO INCLUDES ALL TOPIC OF TRIGNOMETRY OF CLASS 10 WITH PHOTOS AND DERIVATIOM

Surface ARea of Prisms and Cylinders

This document discusses finding the surface area of prisms and cylinders. It provides formulas for calculating surface area of rectangular prisms as S = 2lw + 2lh + 2wh and cylinders as S = 2πr^2 + 2πrh. Examples are given of finding surface areas of various prisms and cylinders using their nets. The document ends with a lesson quiz asking the reader to find surface areas of given figures.

Symmetry

Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement")[1] in everyday language refers to a sense of harmonious and beautiful proportion and balance.[2][3][a] In mathematics, "symmetry" has a more precise definition, that an object is invariant to any of various transformations; including reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart, they are related, so they are here discussed together.
Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, theoretic models, language, music and even knowledge itself.[4][b]
This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and nature; and in the arts, covering architecture, art and music.
The opposite of symmetry is asymmetry.
In geometry[edit]
Main article: Symmetry (geometry)
The triskelion has 3-fold rotational symmetry.
A geometric shape or object is symmetric if it can be divided into two or more identical pieces that are arranged in an organized fashion.[5] This means that an object is symmetric if there is a transformation that moves individual pieces of the object but doesn't change the overall shape. The type of symmetry is determined by the way the pieces are organized, or by the type of transformation:
An object has reflectional symmetry (line or mirror symmetry) if there is a line going through it which divides it into two pieces which are mirror images of each other.[6]
An object has rotational symmetry if the object can be rotated about a fixed point without changing the overall shape.[7]
An object has translational symmetry if it can be translated without changing its overall shape.[8]
An object has helical symmetry if it can be simultaneously translated and rotated in three-dimensional space along a line known as a screw axis.[9]
An object has scale symmetry if it does not change shape when it is expanded or contracted.[10] Fractals also exhibit a form of scale symmetry, where small portions of the fractal are similar in shape to large portions.[11]

Trigonometry

Kartikeya Pandey thanks his teacher Ms. Meha Bhargava and principal Ms. Jasleen Kaur for allowing him to complete a project on trigonometry. He also thanks his parents and friends for their help. The document then provides information on trigonometry including its origins in ancient mathematics, definitions of key terms like sine, cosine, and tangent. It also discusses right triangles, angle measurement in degrees and radians, trigonometric functions, trigonometric identities, and applications of trigonometry.

Triangles

Triangles are three-sided polygons that have three angles and three sides. There are three main types of triangles based on side lengths: equilateral (all sides equal), isosceles (two sides equal), and scalene (no sides equal). The interior angles of any triangle always sum to 180 degrees. Important triangle properties include the exterior angle theorem, Pythagorean theorem, and congruency criteria like SSS, SAS, ASA. Common secondary parts are the median, altitude, angle bisector, and perpendicular bisector. The area of triangles can be found using Heron's formula or other formulas based on side lengths and types of triangles.

Pythagorean Theorem

Pythagoras was an ancient Greek thinker, but he was not the founder of the Pythagorean theorem. That honor goes to his followers, known as the Pythagorean Brotherhood, who established the theorem over 100 years after Pythagoras' death. The Pythagorean theorem states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This relationship has many practical applications in fields like engineering, construction, physics, and astronomy that involve calculating distances.

Ppt on trignometry by damini

This project on trigonometry was designed by two 10th grade students to introduce various topics in trigonometry. It includes sections on the introduction and definition of trigonometry, trigonometric ratios and their names in a right triangle, examples of applying ratios to find unknown sides, reciprocal identities of ratios, types of problems involving calculating ratios and evaluating expressions, value tables for common angles, formulas relating ratios, and main trigonometric identities. The project was created under the guidance of the students' mathematics teacher.

Introduction to trigonometry

This document discusses trigonometric ratios and identities. It defines trigonometric ratios as relationships between sides and angles of a right triangle. Specific ratios are defined for angles of 0, 30, 45, 60, and 90 degrees. Complementary angle identities are examined, showing ratios are equal for complementary angles (e.g. sin(90-A)=cos(A)). Trigonometric identities are derived from the Pythagorean theorem, including cos^2(A) + sin^2(A) = 1, sec^2(A) = 1 + tan^2(A), and cot^2(A) + 1 = cosec^2(A). Examples are provided to demonstrate using identities when

Tests of divisibility

This document provides simple tests and tricks for determining if a number is divisible by certain integers between 2 and 11. It explains that to check divisibility by:
- 2, look at the last digit
- 3, sum the digits and check if divisible by 3
- 4, check if the last two digits are divisible by 4
- 5, check if the last digit is 0 or 5
- 6, check if divisible by both 2 and 3
- 8, check if the last three digits are divisible by 8
- 9, sum the digits and check if divisible by 9
- 10, check if it ends in 0
- 11, take the difference of sums of odd and even place digits.

Trigonometry Exploration

This document summarizes a student project on trigonometry. It was created by a class of 10 students along with their math teacher to help students learn trigonometry through practical experiments and research. The project covers the basics of trigonometry including definitions, history, applications like measuring inaccessible heights, and examples of using trigonometric functions and identities to solve problems.

Trigonometric Ratios of Special Angles.pptx

Trigonometric Ratios of Special Angles.pptx

History of trigonometry2

History of trigonometry2

3 d shapes

3 d shapes

Trigonometry

Trigonometry

Transformation Geometry

Transformation Geometry

medieval European mathematics

medieval European mathematics

The Egyptian Rope Stretchers

The Egyptian Rope Stretchers

Heron’s formula

Heron’s formula

history of trigonometry

history of trigonometry

Ancient math

Ancient math

Introduction to trignometry

Introduction to trignometry

Surface ARea of Prisms and Cylinders

Surface ARea of Prisms and Cylinders

Symmetry

Symmetry

Trigonometry

Trigonometry

Triangles

Triangles

Pythagorean Theorem

Pythagorean Theorem

Ppt on trignometry by damini

Ppt on trignometry by damini

Introduction to trigonometry

Introduction to trigonometry

Tests of divisibility

Tests of divisibility

Trigonometry Exploration

Trigonometry Exploration

Trigonometry

Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. It emerged from applications of geometry to astronomy in the 3rd century BC. Trigonometric functions relate ratios of sides of right triangles to angles and allow for determination of all angles and sides from just one angle and one side. Trigonometry is used in many fields including astronomy, navigation, music, acoustics, optics, engineering, and more due to applications of triangulation and modeling periodic functions.

Trigonometry

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles in triangles. The key concepts are the trigonometric functions sine, cosine, and tangent, which describe ratios of sides of a right triangle. Trigonometry has applications in fields like navigation, music, engineering, and more. It has evolved significantly from its origins in ancient Greece and India, with modern definitions extending it to all real and complex number arguments.

Trigo

Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged from applications of geometry to astronomy in the 3rd century BC. Trigonometric functions relate ratios of sides of a right triangle to its angles, and are now used across many fields including physics, engineering, music, astronomy, and more. Key concepts include defining the sine, cosine, and tangent functions; extending them to angles beyond 90 degrees using the unit circle; and common trigonometric identities and formulas used for solving triangles.

English for Math

Trigonometry is the branch of mathematics that studies relationships involving lengths and angles of triangles. Key concepts include:
- The trigonometric functions (sine, cosine, tangent, etc.) relate angles and side lengths of triangles and are most simply defined using the unit circle.
- Trigonometry has its roots in ancient Greek, Indian, Chinese, Islamic and European mathematics. Important early contributors include Hipparchus, Ptolemy and Aryabhata.
- Right-angled triangle definitions establish the hypotenuse, opposite and adjacent sides and define the trigonometric functions in terms of ratios of these sides.

TRIGONOMETRY

Trigonometry is the branch of mathematics dealing with relationships between the sides and angles of triangles and the calculations of trigonometric functions. It has many applications in fields like navigation, surveying, physics, engineering and more. Some key aspects covered are the definitions of trigonometric functions like sine, cosine and tangent; common trigonometric identities; formulae for calculating unknown sides and angles of triangles; and the history of trigonometry dating back to ancient Greek and Indian mathematicians.

trigonometry and applications

This document provides an overview of trigonometry and its applications. It begins with definitions of trigonometry, its history and etymology. It discusses trigonometric functions like sine, cosine and their properties. It covers trigonometric identities and applications in fields like astronomy, navigation, acoustics and more. It also discusses angle measurement in degrees and radians. Laws of sines and cosines are explained. The document concludes with examples of trigonometric equations and their applications.

Introduction to trigonometry

This document provides an introduction to trigonometry. It defines trigonometry as dealing with relations of sides and angles of triangles. It discusses the history of trigonometry and defines the six trigonometric ratios (sine, cosine, tangent, cosecant, secant, cotangent). It provides the ratios for some specific angles and identities relating the ratios. It describes applications of trigonometry in fields like astronomy, navigation, architecture, and more.

Trigonometry

Trigonometry is the branch of mathematics dealing with relationships between the sides and angles of triangles. It has been used for over 4000 years, originally to calculate sundials and now in fields like navigation, engineering, and astronomy. Trigonometry specifically studies right triangles, where one angle is 90 degrees. The Pythagorean theorem relates the sides of a right triangle, and trigonometric ratios like sine, cosine, and tangent are used to calculate unknown sides and angles based on known values. Trigonometry has many applications in areas involving waves, geometry, and modeling real-world phenomena.

Trigonometry

Trigonometry is the branch of mathematics dealing with relationships between the sides and angles of triangles. It has been used for over 4000 years, originally to calculate sundials and now in fields like astronomy, engineering, and digital imaging. Trigonometry specifically studies right triangles and defines trigonometric functions like sine, cosine, and tangent that relate a triangle's angles and sides. Key concepts include trigonometric ratios, the Pythagorean theorem, trigonometric identities, and applications to problems involving distance, direction, and waves.

Trigonometry

Trigonometry is the branch of mathematics dealing with relationships between the sides and angles of triangles. It has been developed and used for over 4000 years, originating in ancient civilizations for purposes like calculating sundials. A key foundation is the right triangle, where one angle is 90 degrees. Pythagoras' theorem relates the sides of a right triangle, and trigonometric ratios like sine, cosine, and tangent define relationships between sides and angles. Trigonometry has many applications, from astronomy and navigation to engineering, physics, and digital imaging.

trigonometry and application

Trigonometry is derived from Greek words meaning "three angles" and "measure". It deals with relationships between sides and angles of triangles, especially right triangles. The document discusses the history of trigonometry dating back to ancient Egypt and Babylon, and how it advanced through the works of Greek astronomer Hipparchus and Ptolemy. It also discusses the six trigonometric ratios and their formulas, various trigonometric identities, and applications of trigonometry in fields like architecture, engineering, astronomy, music, optics, and more.

Introduction to trigonometry

this is a slide share on introduction of trigonometry this slide share includes every single information about the lesson trigonometry and this is best for class 10

Trigonometry

Trigonometry deals with relationships between sides and angles of triangles, especially right triangles. It has been studied since ancient civilizations over 4000 years ago and is used in many fields today including architecture, astronomy, engineering, and more. Trigonometric functions relate ratios of sides in a right triangle to the angles of the triangle. These functions and their relationships are important tools that allow calculations and problem solving across various domains.

Trigonometry

Trigonometry is the branch of mathematics that deals with triangles and their angles. It originated over 4000 years ago in ancient Egypt, Mesopotamia, and India, where it was used to calculate sundials and circle squares. Key contributors include Hipparchus, who compiled trigonometric tables using sines, and ancient Indian mathematicians who computed sine values. Trigonometry defines functions like sine, cosine, and tangent that relate a triangle's angles and sides. It has many applications, including astronomy, navigation, engineering, acoustics, and more.

PPT on Trigonometric Functions. Class 11

Trigonometry deals with relationships between sides and angles of triangles. It originated in ancient Greece and was used to calculate sundials. Key concepts include trigonometric functions like sine, cosine and tangent that relate a triangle's angles to its sides. Trigonometric identities and angle formulae allow for the conversion between functions. It has wide applications in fields like astronomy, engineering and navigation.

Trigonometry maths school ppt

Trigonometry is the branch of mathematics that deals with triangles, especially right triangles. It has been used for over 4000 years, originally to calculate sundials. Key trigonometric functions are the sine, cosine, and tangent, which relate the angles and sides of a right triangle. Trigonometric identities and the trig functions of complementary angles are also discussed. Trigonometry has many applications, including in astronomy, navigation, engineering, optics, and more. It allows curved surfaces to be approximated in architecture using flat panels at angles.

นำเสนอตรีโกณมิติจริง

Trigonometry deals with relationships between sides and angles of triangles, especially right triangles. It has been used for thousands of years in fields like astronomy, navigation, architecture, engineering, and more modern fields like digital imaging and computer graphics. Trigonometric functions define ratios between sides of a right triangle and are used to solve for unknown sides and angles. Common applications include calculating distances, heights, satellite positioning, and modeling waves and vibrations.

Learning network activity 3

Trigonometry is a branch of mathematics that deals with relationships between the sides and angles of triangles, especially right triangles. It has many applications in fields like astronomy, navigation, engineering, and more. Some key uses of trigonometry include measuring inaccessible heights and distances by using trigonometric functions and properties of triangles formed by angles of elevation or depression. For example, trigonometry can be used to calculate the height of a building or tree by measuring the angle of elevation from a known distance away. It also has applications in measuring distances in astronomy, designing curved architectural structures, and calculating road grades. The document provides examples of various real-world applications of trigonometric concepts.

Trigonometry class10.pptx

This document provides an overview of trigonometry. It defines trigonometry as dealing with relationships between sides and angles of triangles, particularly right triangles. The origins of trigonometry can be traced back 4000 years to ancient civilizations. Key concepts discussed include right triangles, the Pythagorean theorem, trigonometric ratios like sine, cosine and tangent, and applications of trigonometry in fields like construction, astronomy, and engineering. Examples are provided for using trigonometric functions to solve problems involving heights and distances.

presentation_trigonometry-161010073248_1596171933_389536.pdf

Trigonometry deals with relationships between the sides and angles of triangles. It originated over 4000 years ago in ancient civilizations for purposes like calculating sundials. Key concepts include defining right triangles, the Pythagorean theorem relating sides, and trigonometric ratios relating sides to angles. Trigonometry has many applications including construction, astronomy, navigation, and other fields using triangle relationships.

Trigonometry

Trigonometry

Trigonometry

Trigonometry

Trigo

Trigo

English for Math

English for Math

TRIGONOMETRY

TRIGONOMETRY

trigonometry and applications

trigonometry and applications

Introduction to trigonometry

Introduction to trigonometry

Trigonometry

Trigonometry

Trigonometry

Trigonometry

Trigonometry

Trigonometry

trigonometry and application

trigonometry and application

Introduction to trigonometry

Introduction to trigonometry

Trigonometry

Trigonometry

Trigonometry

Trigonometry

PPT on Trigonometric Functions. Class 11

PPT on Trigonometric Functions. Class 11

Trigonometry maths school ppt

Trigonometry maths school ppt

นำเสนอตรีโกณมิติจริง

นำเสนอตรีโกณมิติจริง

Learning network activity 3

Learning network activity 3

Trigonometry class10.pptx

Trigonometry class10.pptx

presentation_trigonometry-161010073248_1596171933_389536.pdf

presentation_trigonometry-161010073248_1596171933_389536.pdf

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Gravitation

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Diabetes

Diabetes

Polynomials

Polynomials

Advertising

Advertising

old age

old age

Chemistry

Chemistry

Diabetes mellitus

Diabetes mellitus

WATER CRISIS “Prediction of 3rd world war”

WATER CRISIS “Prediction of 3rd world war”

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Issue of Shares

My experience my values 7th

My experience my values 7th

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Solid

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Smart class

S107

S107

S104

S104

Mera anubhav meri siksha 7th

Mera anubhav meri siksha 7th

S103

S103

S102

S102

S101

S101

Projectile motion

Projectile motion

Mansi

Mansi

Gravitation

Gravitation

- 2. TRIGONOMETRY Trigonometry (from Greek trigōnon "triangle" + metron "measure") is a branch of mathematics that studies triangles and the relationships between the lengths of their sides and the angles between those sides.
- 3. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves. The field evolved during the third century BC as a branch of geometry used extensively for astronomical studies . It is also the foundation of the practical art of surveying.
- 4. HISTORY Of TRIGONOMETRY Classical Greek mathematicians (such as Euclid and Archimed es) studied the properties of chords and inscribed angles in circles, and proved theorems that are equivalent to modern trigonometric formulae, although they presented them geometrically rather than algebraically.
- 5. The modern sine function was first defined in the Surya Siddhanta, and its properties were further documented by the 5th century Indian mathematician and astronomer Aryabh ata.
- 6. These Greek and Indian works were translated and expanded by medieval Islamic mathematicians. By the 10th century, Islamic mathematicians were using all six trigonometric functions, had tabulated their values, and were applying them to problems in spherical geometry.
- 7. The Father of Trigonometry The first trigonometri c table was apparently compiled by Hipparchus, who is now consequently known as "the father of
- 8. RIGHT TRIANGLE A right triangle or right- angled triangle is a triangle in which one angle is a right angle (that is, a 90- degree angle). The relation between the sides and angles of a right triangle is the basis for trigonometry.
- 9. The side opposite the right angle is called the hypotenuse (side c in the figure above). The sides adjacent to the right angle are called legs. Side a may be identified as the side adjacent to angle B and opposed to (or opposite) angle A, while side b is the side adjacent to angle A and opposed to angle B.
- 10. PYTHAGORAS THEOREM The Pythagorean theorem: The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c).
- 11. If one angle of a triangle is 90 degrees and one of the other angles is known, the third is thereby fixed, because the three angles of any triangle add up to 180 degrees. The two acute angles therefore add up to 90 degrees: they are complementary angles. The shape of a triangle is completely determined, except for similarity, by the angles. TRIGONOMETRIC RATIOS
- 12. Once the angles are known, the ratios of the sides are determined, regardless of the overall size of the triangle. If the length of one of the sides is known, the other two are determined. These ratios are given by the following trigonometric functions of the known angle A, where a, b and c refer to the lengths of the sides in the
- 14. The hypotenuse is the side opposite to the 90 degree angle in a right triangle; it is the longest side of the triangle, and one of the two sides adjacent to angle A. The adjacent leg is the other side that is adjacent to angle A. The opposite side is the side that is opposite to angle A. The terms perpendicular and base are sometimes used for the opposite and adjacent sides respectively. The reciprocals of these functions are named the cosecant (csc or cosec), secant (sec), and cotangent (cot), respectively:
- 16. STANDARD IDENTITIES Identities are those equations that hold true for any value
- 17. REDUCTION FORMULA Sin (90-A) =Cos A Tan (90-A)= Cot A Cosec (90-A)= Sec A
- 18. Calculator1) This calculates the value of trigonometric functions of different angles. 2) First enter whether you want enter the angle in radian or in degree. 3) Then enter the required trigonometric function in the format given below: 4) Enter 1 for Sin 5) Enter 2 for Cosine 6) Enter 3 for tangent 7) Enter 4 for Cosecant 8) Enter 5 for Secant 9) Enter 6 for cotangent 10)Then enter the magnitude of angle.
- 19. Applications of trigonometry Fields that use trigonometry or trigonometric functions include astronomy (especially for locating apparent positions of celestial objects, in which spherical trigonometry is essential) and hence navigation (on the oceans, in aircraft, and in space), music theory, audio synthesis, acoustics, optics, analysis of financial markets, electronics, probability theory, statistics, biology, medical imaging (CAT scans and ultrasound)
- 20. Application of trigonometry in Astronomy 1) Since ancient times trigonometry was used in astronomy 2) The technique triangulation is used to measure the to nearby stars . 3) In 240 B.C, a mathematician named Eratosthenes discovered the radius of the earth using trigonometry and geometry 4) In 2001 , a group of European astronomers did an experiment that started in 1997 about the distance of Venus from the sun.
- 21. conclusion TRIGONOMETRY IS A BRANCH OF MATHEMATICS WITH SEVERAL IMPORTANT AND USEFUL APPLICATIONS.HENCE IT ATTRACTSMORE AND MORE RESEARCHWITH SEVERAL THEORIES PUBLISHED YEAR AFTER YEAR. THANK YOU