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# Trigonometric Ratios and Angles

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#### Trigonometric Ratios and Angles - Lesson Summary

Trigonometry is the branch of mathematics that deals with the study of relationships between sides and angles of a triangle. It is derived from Greek words, Tri meaning  Three , Gon means Angle and Metron means Measure.
Angle
An angle is considered as the figure obtained by rotating a given ray about its end point.

Measure of an angle
The measure of an angle is the amount of rotation from the initial side to the terminal side.

Trigonometric ratio:
The ratio of lengths of two sides of a right angled triangle is called a Trigonometric Ratio. There are six trigonometric ratios

1. sin θ =  opposite side hypotenuse

2. cos θ = adjacent side hypotenuse

3. tan θ = opposite side adjacent side

4. cot θ =  adjacent side opposite side

5. sec θ = hypotenuse adjacent side

6. cosec θ = hypotenuse opposite side

Note: It should be noted that sin θ is an abbreviation for " sin of angle θ", it is not product of sin and θ. Similarly other trigonomertic ratios also.

The relationships between the trigonometric ratios are:

1. sin θ = 1cosec  θ , cosec θ = 1  sin  θ , sin θ x cosec θ = 1.

2. cos θ = 1sec  θ , sec θ = 1cos  θ , cos θ x sec θ = 1.

3. tan θ = 1cot  θ , cot θ =  1tan  θ , tan θ x cot θ = 1.

4. tan θ = sin θ  cos θ   , cot θ = cos θ  sin θ  θ 0° 30° 45° 60° 90° sin θ 0 1 2 1 2 3 2 1 cos θ 1 3 2 1 2 1 2 0 tan θ 0 1 3 1 3 ∝ cot θ ∝ 3 1 1 3 0 sec θ 1 2 3 2 2 ∝ cosec θ ∝ 2 2 2 3 1