91Ó°ÊÓ

In Exercises \(93-98\), solve the given inequality. $$ 3 \arccos (x) \leq \pi $$

In Exercises \(82-128\), verify the identity. Assume that all quantities are defined. $$ \frac{\csc (\theta)}{1+\cot ^{2}(\theta)}=\sin (\theta) $$

Let \(\theta\) be a Quadrant III angle with \(\cos (\theta)=-\frac{1}{5} .\) Show that this is not enough information to determine the sign of \(\sin \left(\frac{\theta}{2}\right)\) by first assuming \(3 \pi<\theta<\frac{7 \pi}{2}\) and then assuming \(\pi<\theta<\frac{3 \pi}{2}\) and computing \(\sin \left(\frac{\theta}{2}\right)\) in both cases.

Find the exact value or state that it is undefined. $$ \arccos \left(\cos \left(\frac{3 \pi}{2}\right)\right) $$

Find the exact value or state that it is undefined. $$ \arccos \left(\cos \left(-\frac{\pi}{6}\right)\right) $$

In Exercises \(82-128\), verify the identity. Assume that all quantities are defined. $$ \frac{\tan (\theta)}{\sec ^{2}(\theta)-1}=\cot (\theta) $$

Without using your calculator, show that \(\frac{\sqrt{2+\sqrt{3}}}{2}=\frac{\sqrt{6}+\sqrt{2}}{4}\)

Find the exact value or state that it is undefined. $$ \arccos \left(\cos \left(\frac{5 \pi}{4}\right)\right) $$

In Exercises \(93-98\), solve the given inequality. $$ \pi>2 \arctan (x) $$

In Exercises \(82-128\), verify the identity. Assume that all quantities are defined. $$ \frac{\cot (\theta)}{\csc ^{2}(\theta)-1}=\tan (\theta) $$