91Ó°ÊÓ

Use the given the information to find the exact values of the remaining circular functions of \(\theta\). \(\csc (\theta)=\frac{25}{24}\) with \(\theta\) in Quadrant I

Graph the oriented angle in standard position. Classify each angle according to where its terminal side lies and then give two coterminal angles, one of which is positive and the other negative. $$ 3 \pi $$

Graph the oriented angle in standard position. Classify each angle according to where its terminal side lies and then give two coterminal angles, one of which is positive and the other negative. $$ -2 \pi $$

Solve the equation, giving the exact solutions which lie in \([0,2 \pi)\). $$ \tan ^{2}(x)=1-\sec (x) $$

Solve the equation, giving the exact solutions which lie in \([0,2 \pi)\). $$ \cot ^{2}(x)=3 \csc (x)-3 $$

Use your calculator to approximate the given value to three decimal places. Make sure your calculator is in the proper angle measurement mode! $$ \csc \left(78.95^{\circ}\right) $$

Use your calculator to approximate the given value to three decimal places. Make sure your calculator is in the proper angle measurement mode! $$ \sec \left(207^{\circ}\right) $$

Use your calculator to approximate the given value to three decimal places. Make sure your calculator is in the proper angle measurement mode! $$ \tan \left(39.672^{\circ}\right) $$

A yo-yo which is \(2.25\) inches in diameter spins at a rate of 4500 revolutions per minute. How fast is the edge of the yo-yo spinning in miles per hour? Round your answer to two decimal places.

In Exercises \(49-54\), use your calculator to approximate the given value to three decimal places. Make sure your calculator is in the proper angle measurement mode! $$ \cos \left(207^{\circ}\right) $$