Give example to show that sine function is an odd function d

Give example to show that sine function is an odd function? (don\'t use specific angles)

Solution

You need to remember the definition of an odd function: f(-x) = -f(x).

If f(x) = sin x => you need to prove that sin(-x) = - sin x

You may consider sin(-x) = sin(0-x).

Applying the following trigonometric formula yields:

sin( 0 - x ) = sin 0*cos x - sin x*cos 0

Replacing sin 0 = 0 and cos 0 = 1 yields:

sin( 0 - x ) = 0*cos x - sin x*1 => sin( 0 - x ) = - sin x

The last line proves that sin(-x) = -sin x, hence the sine function is odd.