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Trigonometric Ratios of 0° and 90°

Trigonometric Ratios of 0° and 90°

OA is a base line.
 


Let OP be a radius line making two different positions such as P1 and P2.

Let OP make angle X with OA.

 

(i)

As X increases, PQ increases in length and hence the value of sin X increases when OP coincides with OQ, sin 0° = 0.

When OP coincides with OB, sin 90° = 1. Thus, cosec 0° = and cosec 90° = 1.


(ii)

As X increases from the value 0° to 90°, OQ decreases in length. Hence cos X decreases from the value 1 to 0 as X increases from 0° to 90° . Thus, cos 0° = 1 and cos 90° = 0. Hence, sec 0° = 1 and sec 90° = .


(iii)

As X increases from 0° to 90°, PQ increases, OQ decreases in length.

Hence tan 0° = 0 and tan 90° = . Thus, cot 0° = and cot 90° = 0.

The standard values of the specific angles are tabulated below:

 

 





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