91Ó°ÊÓ

Find all values of \(\theta\) in the interval of \(\left[0^{\circ}, 360^{\circ}\right)\) that satisfy each equation. Round approximate answers to the nearest tenth of a degree. $$ \sin ^{2} x+9=6 \sin x $$

Find the exact value of each composition without using a calculator or table. $$ \tan (\arctan (1)) $$

Find all values of \(\theta\) in the interval of \(\left[0^{\circ}, 360^{\circ}\right)\) that satisfy each equation. Round approximate answers to the nearest tenth of a degree. $$ \frac{\tan 3 \theta-\tan \theta}{1+\tan 3 \theta \tan \theta}=\sqrt{3} $$

Find all real numbers in the interval \([0,2 \pi]\) that satisfy each equation. $$ \cos (x) \cos (-2 x)-\sin (x) \sin (-2 x)=\frac{\sqrt{3}}{2} $$

Find the inverse of each function and state the domain and range of \(f^{-1}\) $$ f(x)=\sin ^{-1}(x / 2)+3 \text { for }-2 \leq x \leq 2 $$

Find the exact value of each composition without using a calculator or table. $$ \cot (\operatorname{arccot}(0)) $$

Find all real numbers in the interval \([0,2 \pi]\) that satisfy each equation. $$ \sin (x) \cos (-2 x)+\cos (x) \sin (-2 x)=-\frac{1}{2} $$

Find all values of \(\theta\) in the interval of \(\left[0^{\circ}, 360^{\circ}\right)\) that satisfy each equation. Round approximate answers to the nearest tenth of a degree. $$ \frac{\tan 3 \theta+\tan 2 \theta}{1-\tan 3 \theta \tan 2 \theta}=1 $$

Find the inverse of each function and state the domain and range of \(f^{-1}\) $$ f(x)=2 \cos ^{-1}(5 x)+3 \text { for }-\frac{1}{5} \leq x \leq \frac{1}{5} $$

Find all values of \(\theta\) in the interval of \(\left[0^{\circ}, 360^{\circ}\right)\) that satisfy each equation. Round approximate answers to the nearest tenth of a degree. $$ 8 \cos ^{4} \theta-10 \cos ^{2} \theta+3=0 $$