Question

whats is the value of Sin(na) in terms of Sin(a)

Answer 1

WELCOME TO OPENSTUDY

Answer 2

http://en.wikipedia.org/wiki/Trigonometric_formulas#Sine.2C_cosine.2C_and_tangent_of_multiple_angles

has a formula for this but it includes cos^k theta.

Perhaps there is a formula only in terms of Sin, I don't know.

Answer 3

Using DeMoive's theorem you have
\[ (\cos nx + i\sin nx) = (\cos x + i\sin x)^n = \sum_{r = 0}^n \binom{n}{r} (\cos x)^{n-r} (i\sin x)^r\]
find the value of imaginary part.