91Ó°ÊÓ

Use a right triangle to write each expression as an algebraic expression. Assume that \(x\) is positive and that the given inverse trigonometric function is defined for the expression in \(x\). $$ \tan \left(\cos ^{-1} x\right) $$

use reference angles to find the exact value of each expression. Do not use a calculator. $$ \tan 210^{\circ} $$

Find the exact value of each expression. Do not use a calculator. $$ \frac{\tan \frac{\pi}{3}}{2}-\frac{1}{\sec \frac{\pi}{6}} $$

What does it mean to solve a right triangle?

Find a positive angle less than \(360^{\circ}\) or \(2 \pi\) that is coterminal with the given angle. $$ \frac{17 \pi}{5} $$

use reference angles to find the exact value of each expression. Do not use a calculator. $$ \sec 240^{\circ} $$

Use a right triangle to write each expression as an algebraic expression. Assume that \(x\) is positive and that the given inverse trigonometric function is defined for the expression in \(x\). $$ \sin \left(\tan ^{-1} x\right) $$

Exercises \(64-66\) will help you prepare for the material covered in the next section. In each exercise, complete the table of coordinates. Do not use a calculator. $$ y=\frac{1}{2} \cos (4 x+\pi) $$ $$ \begin{aligned} &\begin{array}{lllll} {x} & {-\frac{\pi}{4}} & {-\frac{\pi}{8}} & {0} & {\frac{\pi}{8}} & {\frac{\pi}{4}} \end{array}\\\ &y \end{aligned} $$ After completing this table of coordinates, plot the nine ordered pairs as points in a rectangular coordinate system. Then connect the points with a smooth curve.

Find the exact value of each expression. Do not use a calculator. $$ \frac{1}{\cot \frac{\pi}{4}}-\frac{2}{\csc \frac{\pi}{6}} $$

Explain how to find one of the acute angles of a right triangle if two sides are known.