# Trigonometric Ratios of 0Â° and 90Â°

**Trigonometric Ratios of 0Â° and 90Â°**

OA is a base line.

Let OP be a radius line making two different positions such as P_{1} and P_{2}.

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 0Â° = 0.

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

(ii)

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

(iii)

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

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

The standard values of the specific angles are tabulated below: