91Ó°ÊÓ

Sketch a right triangle corresponding to the trigonometric function of the acute angle \(\boldsymbol{\theta}\). Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of \(\boldsymbol{\theta}\). $$ \cos \theta=\frac{5}{6} $$

Find the period and amplitude. $$ y=3 \sin 10 x $$

Find the point \((x, y)\) on the unit circle that corresponds to the real number \(t\). $$ t=\frac{3 \pi}{4} $$

The point is on the terminal side of an angle in standard position. Determine the exact values of the six trigonometric functions of the angle. $$ (8,15) $$

The point is on the terminal side of an angle in standard position. Determine the exact values of the six trigonometric functions of the angle. $$ (-5,-2) $$

Sketch a right triangle corresponding to the trigonometric function of the acute angle \(\boldsymbol{\theta}\). Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of \(\boldsymbol{\theta}\). $$ \sec \theta=\frac{3}{2} $$

Find the period and amplitude. $$ y=\frac{5}{3} \cos \frac{4 x}{5} $$

Sketch the graph of the function. Include two full periods. $$ y=\frac{1}{3} \tan x $$

Evaluate the expression without using a calculator. $$ \arccos \left(-\frac{1}{2}\right) $$

Find the point \((x, y)\) on the unit circle that corresponds to the real number \(t\). $$ t=\frac{4 \pi}{3} $$