91Ó°ÊÓ

In the yo-yo trick 'Around the World,' the performer throws the yo-yo so it sweeps out a vertical circle whose radius is the yo-yo string. If the yo-yo string is 28 inches long and the yo-yo takes 3 seconds to complete one revolution of the circle, compute the speed of the yo-yo in miles per hour. Round your answer to two decimal places.

In Exercises \(57-86\), find the exact value or state that it is undefined. $$ \sin (\arcsin (-0.42)) $$

Solve the equation. $$ 4 \arctan (3 x-1)-\pi=0 $$

In Exercises \(74-79\), write the given product as a sum. You may need to use an Even/Odd Identity. $$ \sin (2 \theta) \sin (7 \theta) $$

Solve the inequality. Express the exact answer in interval notation, restricting your attention to \(0 \leq x \leq 2 \pi\). $$ 2 \cos (x) \geq 1 $$

The broadcast tower for radio station WSAZ (Home of "Algebra in the Morning with Carl and Jeff") has two enormous flashing red lights on it: one at the very top and one a few feet below the top. From a point 5000 feet away from the base of the tower on level ground the angle of elevation to the top light is \(7.970^{\circ}\) and to the second light is \(7.125^{\circ}\). Find the distance between the lights to the nearest foot.

Solve the inequality. Express the exact answer in interval notation, restricting your attention to \(-\pi \leq x \leq \pi\). $$ \sin (x)>\frac{1}{3} $$

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

Solve the given inequality. $$ 3 \arccos (x) \leq \pi $$

In Exercises \(87-106\), find the exact value or state that it is undefined. $$ \arctan (\tan (\pi)) $$