91Ó°ÊÓ

Find (if possible) the complement and the supplement of each angle. $$\begin{array}{lll}\text { (a) } \frac{\pi}{3} & \text { (b) } \frac{\pi}{4}\end{array}$$

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

Evaluate (if possible) the sine, cosine, and tangent at the real number. $$t=-\frac{7 \pi}{4}$$

Evaluate the expression without using a calculator. $$\sin ^{-1}\left(-\frac{\sqrt{3}}{2}\right)$$

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. $$(-5.4,7.2)$$

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

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 \(\boldsymbol{\theta}\). $$\sec \theta=\frac{17}{7}$$

Evaluate (if possible) the sine, cosine, and tangent at the real number. $$t=-\frac{4 \pi}{3}$$

Evaluate the expression without using a calculator. $$\tan ^{-1}\left(-\frac{\sqrt{3}}{3}\right)$$

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. $$\left(3 \frac{1}{2},-7 \frac{3}{4}\right)$$