Euler's Formula

Question

Use Euler's formula to write the expression as a trigonometric function of θ.

i/2(e^(3iθ)-e^(-3iθ)

I believe the answer to be -sin(3θ). I did this problem a couple of other ways, and eventually was able to conform that this was the correct answer. But I still am unable to use Euler's formula for it.

Answer 1

Euler's formula is simply e^ix = cos x + i sin x.

cos(-x) = cos x but sin (-x) = - sin x

e^3ix = cos 3x + i sin 3x

e^-3ix = cos (-3x) + i sin(-3x) = cos 3x - i sin 3x

The cos terms go out and the sin terms add; I think you missed a sign, i.e. the expression is i sin 3x.