91Ó°ÊÓ

For the simple harmonic motion described by the trigonometric function, find (a) the maximum displacement, (b) the frequency, (c) the value of \(d\) when \(t=5,\) and (d) the least positive value of \(t\) for which \(d=0 .\) Use a graphing utility to verify your results. $$ d=9 \cos \frac{6 \pi}{5} t $$

Rewrite each angle in radian measure as a multiple of \(\pi\). (Do not use a calculator.) (a) \(30^{\circ}\) (b) \(45^{\circ}\)

Find the exact value of the expression. (Hint: Sketch a right triangle.) $$ \cos \left(\tan ^{-1} 2\right) $$

Evaluate the sine, cosine, and tangent of the angle without using a calculator. $$ -150^{\circ} $$

Use the graph of the function to determine whether the function is even, odd, or neither. Verify your answer algebraically. $$ f(x)=\sec x $$

Find the values of \(\theta\) in degrees \(\left(0^{\circ}<\theta<90^{\circ}\right)\) and radians \((0<\theta<\pi / 2)\) without the aid of a calculator. $$ \text { (a) } \sin \theta=\frac{1}{2} $$

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.) $$ \sec (-22.8) $$

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.) $$ \cot (-0.9) $$

Rewrite each angle in radian measure as a multiple of \(\pi\). (Do not use a calculator.) (a) \(315^{\circ}\) (b) \(120^{\circ}\)

Find the values of \(\theta\) in degrees \(\left(0^{\circ}<\theta<90^{\circ}\right)\) and radians \((0<\theta<\pi / 2)\) without the aid of a calculator. (a) \(\cos \theta=\frac{\sqrt{2}}{2}\) (b) \(\tan \theta=1\)