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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.
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