discussed the values of trigonometric ratios for °, °, °, ° and °. The values of trigonometric functions for these angles are same as that of trigonometric ratios studied in earlier classes. Thus, we have the following table: ° π π π π π π π sin – cos – tan The values of cosec x , sec x and cot x are the reciprocal of the values of sin x , cos x and tan x , respectively. .
. Sign of trigonometric functions Let P ( a, b ) be a point on the unit circle with centre at the origin such that ∠ AOP = x . If ∠ AOQ = – x , then the coordinates of the point Q will be ( a , – b ) (Fig . ).
Therefore cos (– x ) = cos x and sin (– x ) = – sin x Since for every point P ( a, b ) on the unit circle, – ≤ a ≤ and Fig . MATHEMATICS – ≤ b ≤ , we have – ≤ cos x ≤ and – ≤ sin x ≤ for all x . We have learnt in previous classes that in the first quadrant ( < x < π ) a and b are both positive, in the second quadrant ( π < x < π ) a is negative and b is positive, in the third quadrant ( π < x < π ) a and b are both negative and in the fourth quadrant ( π < x < π ) a is positive and b is negative. Therefore, sin x is positive for < x < π , and negative for π < x < π .
Similarly, cos x is positive for < x < π , negative for π < x < π and also positive for π < x < π . Likewise, we can find