91Ó°ÊÓ

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

Rewrite each angle in degree measure. (Do not use a calculator.) (a) \(\frac{3 \pi}{2}\) (b) \(\frac{7 \pi}{6}\)

\(g\) is related to a parent function \(f(x)=\sin (x)\) or \(f(x)=\cos (x)\) (a) Describe the sequence of transformations from \(f\) to \(g\). (b) Sketch the graph of \(g\). (c) Use function notation to write \(g\) in terms of \(f\). $$ g(x)=\sin (4 x-\pi) $$

Evaluate the sine, cosine, and tangent of the angle without using a calculator. $$ \frac{5 \pi}{4} $$

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) \(\csc \theta=\frac{2 \sqrt{3}}{3}\) (b) \(\sin \theta=\frac{\sqrt{2}}{2}\)

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

Find the exact value of the expression. (Hint: Sketch a right triangle.) $$ \sec \left[\arctan \left(-\frac{3}{5}\right)\right] $$

Evaluate the sine, cosine, and tangent of the angle without using a calculator. $$ \frac{7 \pi}{6} $$

Use the graph of the function to determine whether the function is even, odd, or neither. Verify your answer algebraically. $$ f(x)=x^{2}-\sec x $$

Determine whether the statement is true or false. Justify your answer. $$ \tan a=\tan (a-6 \pi) $$