Question

How do you simplify `f(theta)=sin3theta-cos3theta` to trigonometric functions of a unit `theta`?

Answer 1

`f(t) = 3(sin t - cos t)+ 4(cos^3 t - sin^3 t)`

Explanation:

Use the trig identities:
`sin 3t = 3sin t - 4sin^3 t`
`cos 3t = 4cos^3 t - 3cos t`
`f(t) = sin 3t - cos 3t = 3(sin t - cos t) + 4(cos^3 t - sin^3 t)`