Question

How do you express `sin^4theta - sin^3theta + cos^2theta` in terms of non-exponential trigonometric functions?

Answer 1

Transform trig expression.

Explanation:

Apply the 2 trig identities:
`cos ^2 t = (1 + cos 2t)/2`
`sin^2 t = (1 - cos 2t)/2`
`sin^4 t - sin^3 t + cos^2 t = sin^2 t(sin t)(sin t - 1) + cos ^2 t =`
`= ((1 - cos 2t)/2) (sin t - 1)sin t + (1 + cos 2t)/2`