91Ó°ÊÓ

In Exercises \(87-92,\) solve the inequality. Express the exact answer in interval notation, restricting your attention to \(-2 \pi \leq x \leq 2 \pi\). $$ \cos (x) \leq \frac{5}{3} $$

In Exercises \(87-92,\) solve the inequality. Express the exact answer in interval notation, restricting your attention to \(-2 \pi \leq x \leq 2 \pi\). $$ \cot (x) \geq 5 $$

Find the exact value or state that it is undefined. $$ \arcsin \left(\sin \left(\frac{3 \pi}{4}\right)\right) $$

In Exercises \(82-128\), verify the identity. Assume that all quantities are defined. $$ \frac{1+\sin (\theta)}{\cos (\theta)}=\sec (\theta)+\tan (\theta) $$

Find the exact value or state that it is undefined. $$ \arcsin \left(\sin \left(\frac{11 \pi}{6}\right)\right) $$

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

In Exercises \(87-92,\) solve the inequality. Express the exact answer in interval notation, restricting your attention to \(-2 \pi \leq x \leq 2 \pi\). $$ \tan ^{2}(x) \geq 1 $$

In Exercises \(82-128\), verify the identity. Assume that all quantities are defined. $$ \frac{1-\cos (\theta)}{\sin (\theta)}=\csc (\theta)-\cot (\theta) $$

In Exercises \(87-92,\) 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 \(x\).