sin x repeats after an interval of π . Therefore sin π = sin ( π + π ) = sin π = . TRIGONOMETRIC FUNCTIONS Example Find the value of cos (– °). Solution We know that values of cos x repeats after an interval of π or °.
Therefore, cos (– °) = cos (– ° + × °) = cos (– ° + °) = cos ° = . EXERCISE . Find the values of other five trigonometric functions in Exercises to . .
cos x = – , x lies in third quadrant. . sin x = , x lies in second quadrant. .
cot x = , x lies in third quadrant. . sec x = , x lies in fourth quadrant. .
tan x = – , x lies in second quadrant. Find the values of the trigonometric functions in Exercises to . . sin ° .
cosec (– °) . tan π . sin (– π ) . cot (– π ) .
Trigonometric Functions of Sum and Difference of Two Angles In this Section, we shall derive expressions for trigonometric functions of the sum and difference of two numbers (angles) and related expressions. The basic results in this connection are called trigonometric identities . We have seen that . sin (– x ) = – sin x .
cos (– x ) = cos x We shall now prove some more results: MATHEMATICS . cos ( x + y ) = cos x cos y – sin x sin y Consider the unit circle with centre at the origin. Let x be the angle P OP and y be the angle P OP . Then ( x + y ) is the angle P OP .
Also let (– y ) be the angle P OP . Therefore, P , P , P and P will