What is -sin^4theta in terms of non-exponential trigonometric functions?

1 Answer
Mar 18, 2016

= -3/8 - (cos 4t)/8 + (cos 2t)/2

Explanation:

2sin^2 t = (1 - cos 2t).
Square the 2 sides:
4sin^4 t = (1 - cos 2t)^2 = 1 + cos^2 2t - 2cos 2t
Replace cos^2 2t by (1 + cos 4t)/2
4sin^4t = 1 + 1/2 + cos (4t)/2 - 2cos 2t =
3/2 + (cos (4t)/2) - 2cos 2t
Divide both sides by -4 -->

- sin^4 t = - 3/8 - (cos 4t)/8 + (cos 2t)/2