Question

Sin (3 theta) = -1 what is the solution set

Answer 1

`\sin(3\theta)=-1\\\\subtitute\ 3\theta=\alpha\\\\therefore\\\\\sin(3\theta)=\sin\alpha=-1\iff\alpha=270^o+360^o\cdot k\ or\ equivalent\ \alpha=(3)/(2)\pi+2k\pi`


`3\theta=270^o+360^o\cdot k\ \ \ \ |divide\ both\ sides\ by\ 3\\\\\boxed{\theta=90^o+120^o\cdot k}\\\\equivalent\\\\3\theta=(3)/(2)\pi+2k\pi\ \ \ \ |divid\ both\ sides\ by\ 3\\\\\boxed{\theta=(1)/(2)\pi+(2)/(3)k\pi}`