# Trignometry in daily life

2 de Feb de 2014
1 de 11

### Trignometry in daily life

• 1. USE OF TRIGONOMETRY IN REAL LIFE SUPREIYA CLASS : X - A
• 2. WHAT IS TRIGONOMETRY?  Trigonometry in basic words is the mathematics of triangles and trigonometric functions.  The word “Trigonometry” comes from the Greek words: ‘Trigonon’ meaning ‘triangle’ and ‘metron’ meaning a ‘measure’.  In a broader sense, trigonometry is that branch if mathematics which deals with the measurement of the sides and the angles of a triangle and the problems allied with angles.
• 3. ORIGIN OF ‘SINE’ “Trigonometry is not the work of any one person or nation. Its history spans thousands of years and has touched every major civilization .”  The first use of the idea of ‘sine’ in the way we use it today was in the work Aryabhatiyam by Aryabhata in A.D. 500.  Aryabhata used the word ‘ardha-jya ’ for the half chord which came to be known as ‘jiva ’ in due course.  Later, ‘jiva ’ came to be known as ‘sinus’ and later as ‘sine ’.  An English Professor Edmund Gunter (1581-1626) first used the abbreviated notation ‘sin ’ . Aryabhata A.D. 476-550
• 4. COSINE AND TANGENT  The origin of the terms ‘ cosine’ and ‘tangent’ was much later. The cosine function arose from the need to compute the sine of the complementary angle.  Aryabhata called ‘kotijya’.  The name cosinus originated with Edmund Gunter. In 1674, the English Mathematician Sir Jonas Moore first used the abbreviated notation ‘cos’ Edmund Gunter (1581 –1626)
• 5. THE TRIGONOMETRIC RATIOS Abbr. Descriptio n Sine sin Opposite Cosine cos Tangent tan Cotangent The Cosecant, Secant, and Cotangent are the Reciprocals of the Sine, Cosine,and Tangent respectively . Function cot Secant Note: The formulas provided are in respect to the picture. sec Cosecan cosec t Hypotenus e Adjacent Hypotenus e Opposite Adjacent Adjacent Opposite Hypotenus e Adjacent Hypotenus e
• 6. THE TRIGONOMETRIC VALUES Angle A 0o 30o 45o 60o 90o sin A 0 1 1 √3 1 1 2 √3 √2 1 2 1 0 0 2 1 √2 1 2 √3 √3 2 √2 2 2 √2 √3 2 √3 √3 1 1 cos A tan A cosec A sec A cot A Not Defined 1 Not Defined √3 Not Defined 1 Not Defined 0
• 7. HOW TO USE TRIGONOMETRY IN REAL The LIFE given is elaborated as follows: project ?  Objective : To find the angle of elevation of a room .  Knowledge Required : 1.Trigonometric Ratios 2. Trigonometric Values (acute angles)  Materials Required : 1. A meter stick 2. A measuring tape
• 8. PERFORMING THE TASK !!  Take the meter stick and put it horizontally on the wall to measure the length .  Now, with the help of an adult measure the diagonal distance (hypotenuse) of your room.  Record the length in centimeters and convert it into meters.  Take the ratio of the length of the stick to the diagonal distance to your room.  Use the trigonometric ratios to find out the angle of elevation of your room !!
• 9. THE MUCH AWAITED RESULT  I performed the activity mentioned and since I took the ratio of wall to the diagonal my ratio was as follows : Perpendicular (opposite) Hypotenuse  We already know that this value is equal to sin.  Now the values I got were: Perpendicular = 6 mts. Hypotenuse = 12mts.
• 10. THERE’S THE ANSWER!!!  Sin A = Perpendicular Hypotenuse = (Putting the Values) 6 12 Sin A = 1 2 Sin A = Sin 30 o Angle of Elevation = 30o