91Ó°ÊÓ

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

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. $$ 12 \cos ^{2} \theta+\cos \theta-6=0 $$

Find the exact value of each composition without using a calculator or table. $$ \sec ^{-1}(\sec (\pi / 3)) $$

Find the inverse of each function and state the domain and range of \(f^{-1}\) $$ f(x)=4 \cos (\pi(x-2))+1 \text { for } 2 \leq x \leq 3 $$

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. $$ \sin x \cos x+2 \cos x=3 \sin x+6 $$

Find all real numbers in the interval \([0,2 \pi]\) that satisfy each equation. $$ \sin (x)+\sin (3 x)=0 $$

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

Find the exact value of each composition without using a calculator or table. $$ \arcsin (\sin (3 \pi / 4)) $$

Find the inverse of each function and state the domain and range of \(f^{-1}\) $$ f(x)=\cos ^{-1}(x+4) \text { for }-5 \leq x \leq-3 $$

Find the exact value of each composition without using a calculator or table. $$ \arccos (\cos (-\pi / 3)) $$