91Ó°ÊÓ

Evaluate the trigonometric function using its period as an aid. $$\sin \frac{19 \pi}{6}$$

Rewrite each angle in radian measure as a multiple of \(\pi .\) (Do not use a calculator.) (a) \(-60^{\circ}\) (b) \(144^{\circ}\)

Sketch the graphs of \(f\) and \(g\) in the same coordinate plane. (Include two full periods.) $$\begin{array}{l} f(x)=4 \sin \pi x \\ g(x)=4 \sin \pi x-3 \end{array}$$

Evaluate the trigonometric function using its period as an aid. $$\sin \left(-\frac{8 \pi}{3}\right)$$

Sketch the graph of the function. (Include two full periods.) $$y=-\sec \pi x+1$$

Use a calculator to evaluate the expression. Round your result to two decimal places. $$\tan ^{-1}\left(-\frac{95}{7}\right)$$

Use a calculator to evaluate each function. Round your answers to four decimal places. (Be sure the calculator is in the correct mode.) (a) sec \(42^{\circ} 12^{\prime}\) (b) \(\csc 48^{\circ} 7^{\prime}\)

A ship leaves port at noon and has a bearing of \(\mathrm{S} 29^{\circ} \mathrm{W}\). The ship sails at 20 knots. (a) How many nautical miles south and how many nautical miles west will the ship have traveled by 6: 00 P.M.? (b) At 6: 00 e.m., the ship changes course to due west. Find the ship's bearing and distance from the port of departure at 7: 00 P.M.

Use a calculator to evaluate the expression. Round your result to two decimal places. $$\tan ^{-1}(-\sqrt{372})$$

Sketch the graph of the function. (Include two full periods.) $$y=\frac{1}{4} \csc \left(x+\frac{\pi}{4}\right)$$