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.)
tan θ sin θ + sin θ = 0

Answer 1

\[\tan \theta \sin \theta+\sin \theta=\sin \theta (\tan \theta+1)=0\]which leads to\[\sin \theta=0 \to \theta=n \pi; n=0,1,2,...\]\[\tan \theta=-1 \to \theta={3\pi \over4}+n \pi;n=0,1,2,...\]

Answer 2

oh, you wanted "k" where I put "n", so you can change that.

Answer 3

\[\theta=\left\{ \pi k, {3\pi \over4}+k \pi \right\}\]

Answer 4

Thanks :)