91Ó°ÊÓ

Convert the angle measure from radians to degrees. Round to three decimal places. $$ -2 $$

Fill in the blank. $$ \arcsin \frac{\sqrt{36-x^{2}}}{6}=\arccos (\quad), \quad 0 \leq x \leq 6 $$

Convert the angle measure from radians to degrees. Round to three decimal places. $$ -0.57 $$

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.) $$ \cot 178^{\circ} $$

Graph the functions \(f\) and \(g\). Use the graphs to make a conjecture about the relationship between the functions. $$ f(x)=\cos ^{2} \frac{\pi x}{2}, \quad g(x)=\frac{1}{2}(1+\cos \pi x) $$

Determine whether the statement is true or false. Justify your answer. $$ \cot ^{2} 10^{\circ}-\csc ^{2} 10^{\circ}=-1 $$

Determine whether the statement is true or false. Justify your answer. $$ \frac{\sin 60^{\circ}}{\sin 30^{\circ}}=\sin 2^{\circ} $$

Convert each angle measure to decimal degree form without using a calculator. Then check your answers using a calculator. (a) \(54^{\circ} 45^{\prime}\) (b) \(-128^{\circ} 30^{\prime}\)

Use a graphing utility to graph the function and the damping factor of the function in the same viewing window. Describe the behavior of the function as \(x\) increases without bound. $$ g(x)=e^{-x^{2} / 2} \sin x $$

Use a graphing utility to graph \(y_{1}\) and \(y_{2}\) in the interval \([-2 \pi, 2 \pi]\). Use the graphs to find real numbers \(x\) such that \(y_{1}=y_{2}\). $$ \begin{array}{l} y_{1}=\sin x \\ y_{2}=-\frac{1}{2} \end{array} $$