Question

Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.)

csc θ(2 cos θ − 1) = 0

Answer 1

`-1\le\sin\theta\le1\implies(\csc\theta\le-1)\cup(\csc\theta\ge1)`

which means
`\csc\theta=0` has no solution, and we can omit that factor.

This leaves us with


`2\cos\theta-1=0\implies\cos\theta=\frac12`

which occurs for
`\theta=\pm\frac\pi3+2n\pi`.