91Ó°ÊÓ

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

Evaluate the sine, cosine, and tangent of the angle without using a calculator. $$ -840^{\circ} $$

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. $$ d=\frac{1}{2} \cos 20 \pi t $$

Find the exact value of the expression. (Hint: Sketch a right triangle.) $$ \sin \left(\cos ^{-1} \frac{\sqrt{5}}{5}\right) $$

Sketch the graph of the function. (Include two full periods.) $$ y=3 \cos (x+\pi)-3 $$

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. $$ d=\frac{1}{4} \sin 6 \pi t $$

Rewrite each angle in radian measure as a multiple of \(\pi\). (Do not use a calculator.) (a) \(-20^{\circ}\) (b) \(-60^{\circ}\)

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

Find the exact value of the expression. (Hint: Sketch a right triangle.) $$ \cos \left(\arcsin \frac{5}{13}\right) $$

Evaluate the sine, cosine, and tangent of the angle without using a calculator. $$ \frac{2 \pi}{3} $$