Question

Find all solutions for 3sin^2 θ +16 sin θ -35=0. (Use 'k' as any integer)

Answer 1

Replace sin(theta) with x

\[3x ^{2}+16x-35=0\]

\[(3x - 5)(x + 7)\=0\]

Answer 2

Now replace back:
\[(3\sin \theta-5)(\sin \theta+7)=0\]
So either
\[3\sin \theta-5=0\] or \[\sin \theta+7=0\]
\[\sin \theta \neq-7\] so \[3\sin \theta=5\]
\[\sin \theta=\frac{ 5 }{ 3 }\] but this can't be either since \[-1\le \sin \theta \le1\]

It seems as though we have "No Solution"