Question

express sin(6t) as an exponential function?

Answer 1

Use\[\sin\theta=\frac{e^{i\theta}-e^{-i\theta}}{2i}\]

Answer 2

so it would just be \[\frac{ e ^{i6t}-e ^{-i6t} }{ 2i }\] or is the denominator multiplied by n as well?

Answer 3

that's right, you can simplify further, with \(1/i=-i\),

Answer 4

ahh thankyou unkleRhaukus! been bugging me for a long time haha

Answer 5

if your going back the other way ,
use \[e^{i\theta}=\cos\theta+i\sin\theta\]