91Ó°ÊÓ

Determine two coterminal angles (one positive and one negative) for each angle. Give your answers in radians. $$\begin{array}{ll}\text { (a) } \frac{\pi}{6} & \text { (b) } \frac{7 \pi}{6}\end{array}$$

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. $$(-4,10)$$

Find the period and amplitude. $$y=\frac{5}{2} \cos \frac{x}{4}$$

Determine two coterminal angles (one positive and one negative) for each angle. Give your answers in radians. $$\text { (a) } \frac{2 \pi}{3} \quad \text { (b) }-\frac{9 \pi}{4}$$

Evaluate the expression without using a calculator. $$\arcsin \frac{\sqrt{2}}{2}$$

evaluate (if possible) the sine, cosine, and tangent at the real number. $$t=-\frac{\pi}{4}$$

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 \(\boldsymbol{\theta}\). $$\tan \theta=\frac{4}{5}$$

Sketch the graph of the function. (Include two full periods.) $$y=\tan 4 x$$

Find the period and amplitude. $$y=\frac{1}{4} \sin 2 \pi x$$

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 \(\boldsymbol{\theta}\). $$\sin \theta=\frac{1}{5}$$