How do you write sin(4x) in terms of sin(x)? Thank you!

1 Answer
Sep 24, 2017

sin4x=4(sinx-2sin^3x)sqrt(1-sin^2x)

Explanation:

sin4x=2sin2xcos2x

= 2xx2sinxcosx xx(1-2sin^2x

= 4sinxcosx-8sin^3xcosx

This is generally used expansion for sin4x, however to write in terms of pure sinx, one can substitute cosx with sqrt(1-sin^2x), although there could be issues regarding choosing appropriate sign based on which quadrant x falls.

In such a case sin4x=4(sinx-2sin^3x)sqrt(1-sin^2x)