Question

Express the quantity in a form that does not involve powers of the trigonometric function.
sin^6 θ

Answer 1

are we allowed to use a formula derived from Euler's formula?
\[\sin(\theta) = \frac{e^{i\theta}-e^{-i\theta}}{2i}\]
im churning out a solution right now that uses that fact.

Answer 2

i know its really sloppy >.<
final answer is:
\[-\frac{1}{32}(\cos(6\theta)-6\cos(4\theta)+15\cos(2\theta)-10)\]

Answer 3

you turn the sin^6 into that formula i posted above, expand, and then collect all the terms that go together to make cos's:
\[\cos(n\theta) = \frac{e^{n i\theta}+e^{-n i\theta}}{2}\]

Answer 4

I struggled with that problem for hours and couldn't get it. Thank so much!!