91Ó°ÊÓ

In Exercises \(87-106\), find the exact value or state that it is undefined. $$ \arcsin \left(\sin \left(\frac{11 \pi}{6}\right)\right) $$

Verify the identity. Assume that all quantities are defined. $$ \frac{\cos (\theta)}{1-\sin ^{2}(\theta)}=\sec (\theta) $$

Solve the inequality. Express the exact answer in interval notation, restricting your attention to \(-2 \pi \leq x \leq 2 \pi\). $$ \sin (2 x) \geq \sin (x) $$

If \(\tan (\theta)=\frac{x}{7}\) for \(-\frac{\pi}{2}<\theta<\frac{\pi}{2}\), find an expression for \(\sin (2 \theta)\) in terms of \(x\).

In Exercises \(87-106\), find the exact value or state that it is undefined. $$ \arcsin \left(\sin \left(\frac{4 \pi}{3}\right)\right) $$

If \(\sec (\theta)=\frac{x}{4}\) for \(0<\theta<\frac{\pi}{2}\), find an expression for \(\ln |\sec (\theta)+\tan (\theta)|\) in terms of \(x\).

Solve the inequality. Express the exact answer in interval notation, restricting your attention to \(-2 \pi \leq x \leq 2 \pi\). $$ \cos (2 x) \leq \sin (x) $$

In Exercises \(87-106\), find the exact value or state that it is undefined. $$ \arccos \left(\cos \left(\frac{\pi}{4}\right)\right) $$

Verify the identity. Assume that all quantities are defined. $$ \frac{\sin (\theta)}{1-\cos ^{2}(\theta)}=\csc (\theta) $$

In Exercises \(87-106\), find the exact value or state that it is undefined. $$ \arccos \left(\cos \left(\frac{\pi}{4}\right)\right) $$