Basic Trigonometry

1. Basic Trigonometry
Technical English Ι
Sinan ÜLKER
31/10/2014

2. What is Trigonometry
● As a word, trigonometry comes from Greek
● The words are “trigōnon” and “metron”
● Wikipedia says :
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– Trigonometry (from Greek trigōnon, "triangle" and metron, "measure"[) is
a branch of mathematics that studies relationships involving lengths and
angles of triangles. The field emerged during the 3rd century BC from
applications of geometry to astronomical studies.

3. Parts of a Right Triangle
● |AB| Hypotenuse will always be the longest side.
● |BC| Adjacent side is the side next to Angle x.
● |AC| Opposite side is the side that is on the opposite side of the triangle from Angle x.
A
B C
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4. Trigonometric Ratios
A
B C
Sinx =
Opposite
Hypotenuse
Cosx =
Adjacent
Hypotenuse
Tanx =
Opposite
Adjacent
● Sine
● Cosine
● Tangent
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5. SOHCAHTOA
To memorize the equations there is a catchy phrase : socahtoa
● SOH : Sine is Opposite over Hypotenuse
● CAH : Cosine is Adjacent over Hypotenuse
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● TOA : Tangent is Opposite over Hypotenuse

6. Important Angles
ANGLE Sin Cos Tan = Sin/Cos
30 1/√3 = √3/3
45 1
60 √3
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7. Pythagoras Theorem
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● Pythagoras' Theorem says that for a right angled triangle, the
square of the long side equals the sum of the squares of the
other two sides:
x² + y² = 1²
Also known as :
the equation of the unit circle
Since x = cos, y = sin
cos²x + sin²x = 1

8. Trigonometric Ratios
Cscx =
Hypotenuse
Opposite
● Secant
● Cosecant
● Cotangent
Secx =
Hypotenuse
Adjacent
Cotx =
Adjacent
Opposite
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9. Unit circle
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In mathematics, a unit circle is a circle with a radius of 1. Frequently, especially in
trigonometry, the unit circle is the circle of radius one centered at the origin (0, 0) in
the Cartesian coordinate system in the Euclidean plane

10. Trig Functions On Unit Circle
Every
trigonometric
function has a
place on the unit
circle
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11. Sine and Cosine on Unit Circle
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Sum and Difference of Trig Functions
We can calculate
sum and diffirence
of trig functions by
this equations

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Products of Trigonometric Functions
We can calculate
products of trig
functions by this
equations

14. Reciprocal identities
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All these trig identities can be derived from first
principles.

15. Links
● Wikipedia
● Google
● http://www.mathopenref.com/
● http://www.efunda.com/math/
● https://www.khanacademy.org/
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Note : You can also find this presentation at : blog.sinanulker.com