91Ó°ÊÓ

In \(3-14,\) find the exact values of \(\theta\) in the interval \(0^{\circ} \leq \theta < 360^{\circ}\) that satisfy each equation. $$ 2 \cos ^{2} \theta=\sin \theta+2 $$

In \(9-14,\) find the exact values for \(\theta\) in the interval \(0 \leq \theta<2 \pi\) $$ \sin \theta+\sqrt{2}=\frac{\sqrt{2}}{2} $$

In \(11-18,\) find all radian measures of \(\theta\) in the interval \(0 \leq \theta \leq 2 \pi\) that make each equation true. Express your answers in terms of \(\pi\) when possible; otherwise, to the nearest hundredth. $$ 2 \sin 2 \theta+\sin \theta=0 $$

In \(9-14,\) find, to the nearest tenth of a degree, the values of \(\theta\) in the interval \(0^{\circ} \leq \theta<360^{\circ}\) that satisfy each equation. $$ \tan ^{2} \theta+4 \tan \theta-12=0 $$

In \(9-14,\) find the exact values for \(\theta\) in the interval \(0 \leq \theta<2 \pi\) $$ 3 \csc \theta+5=\csc \theta+9 $$

In \(11-18,\) find all radian measures of \(\theta\) in the interval \(0 \leq \theta \leq 2 \pi\) that make each equation true. Express your answers in terms of \(\pi\) when possible; otherwise, to the nearest hundredth. $$ 5 \sin ^{2} \theta-4 \sin \theta+\cos 2 \theta=0 $$

In \(3-14,\) find the exact values of \(\theta\) in the interval \(0^{\circ} \leq \theta < 360^{\circ}\) that satisfy each equation. $$ \cot ^{2} \theta=\csc \theta+1 $$

In \(3-14\) , use the quadratic formula to find, to the nearest degree, all values of \(\theta\) in the interval \(0^{\circ} \leq \theta<360^{\circ}\) that satisfy each equation. $$ \frac{\sin \theta}{2}=\frac{3}{\sin \theta+2} $$

In \(9-14,\) find the exact values for \(\theta\) in the interval \(0 \leq \theta<2 \pi\) $$ 4(\cot \theta+1)=2(\cot \theta+2) $$

In \(3-14,\) find the exact values of \(\theta\) in the interval \(0^{\circ} \leq \theta < 360^{\circ}\) that satisfy each equation. $$ 2 \sin ^{2} \theta-\tan \theta \cot \theta=0 $$