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. $$ \tan ^{2} \theta-\cot ^{2} \theta=0 $$

Find the inverse of each function and state the domain and range of \(f^{-1}\) $$ f(x)=3 \cos (2 x)+1 \text { for } 0 \leq x \leq \frac{\pi}{2} $$

Find the exact value of each composition without using a calculator or table. $$ \sin ^{-1}(\cos (2 \pi / 3)) $$

Find the inverse of each function and state the domain and range of \(f^{-1}\) $$ f(x)=3+\tan (\pi x) \text { for }-\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. $$ \tan ^{2} \theta-2 \tan \theta-1=0 $$

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. $$ \cot ^{2} \theta-4 \cot \theta+2=0 $$

Find the inverse of each function and state the domain and range of \(f^{-1}\) $$ f(x)=1+\tan \left(\frac{\pi}{2} x\right) \text { for }-1

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

Find the exact value of each composition without using a calculator or table. $$ \tan ^{-1}(\sin (\pi / 2)) $$

Find the exact value of each composition without using a calculator or table. $$ \cot ^{-1}(\cot (\pi / 6)) $$