91Ó°ÊÓ

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

Find (if possible) the complement and the supplement of each angle. (a) \(\frac{\pi}{12}\) (b) \(\frac{11 \pi}{12}\)

Sketch the graph of the function. (Include two full periods.) $$y=-\frac{1}{2} \sec x$$

Describe the relationship between the graphs of \(f\) and \(g .\) Consider amplitude, period, and shifts. $$\begin{array}{l} f(x)=\sin x \\ g(x)=\sin (x-\pi) \end{array}$$

Use a graphing utility to graph \(f\) \(g,\) and \(y=x\) in the same viewing window to verify geometrically that \(g\) is the inverse function of \(f .\) (Be sure to restrict the domain of \(f\) properly.) $$f(x)=\cos x, \quad g(x)=\arccos x$$

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 \(\boldsymbol{\theta}\). $$\cot \theta=3$$

Evaluate (if possible) the sine, cosine, and tangent at the real number. $$t=\frac{11 \pi}{6}$$

State the quadrant in which \(\boldsymbol{\theta}\) lies. $$\sin \theta>0 \text { and } \cos \theta>0$$

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 \(\boldsymbol{\theta}\). $$\csc \theta=9$$

Length The sun is \(20^{\circ}\) above the horizon. Find the length of a shadow cast by a park statue that is 12 feet tall.