Question

Solve Cos(2 theta) = -1/2

Answer 1

\(\bf cos(2\theta)=-\cfrac{1}{2}\implies 2cos^2(\theta)-1=-\cfrac{1}{2}\)

and simplify it like the previous one, and take \(\Large cos^{-1}\) to get \(\theta\) like in the previous one

Answer 2

thank you can you answer another question? Sin(3theta)=-1?

Answer 3

hmmm

Answer 4

well... for one I need to dash in a few secs

but the triple angle identity wouild be \(\bf {\color{brown}{ sin(3\theta)\to 3sin(\theta)-4sin^3(\theta)}}\)

though I didn't find much headway there
so I'd instead split it in a 2 angle sum or
\(\bf sin(3\theta)=-1\qquad
\begin{cases}
sin(\theta+2\theta)\\
sin(\theta)cos(2\theta)+cos(2\theta)sin(\theta)\\
sin(\theta)[1-2sin^2(\theta)]+cos(\theta)[2sin(\theta)cos(\theta)]
\end{cases}\)