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

1 Answer | Add Yours

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

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.

We’ve answered 318,959 questions. We can answer yours, too.

Ask a question