91Ó°ÊÓ

Find the period and graph the function. $$y=\frac{1}{2} \sec \left(x-\frac{\pi}{6}\right)$$

Find the value of each of the six trigonometric functions (if it is defined) at the given real number \(t\). Use your answers to complete the table. $$t=\frac{\pi}{2}$$ (TABLE CAN'T COPY).

Find the terminal point \(P(x, y)\) on the unit circle determined by the given value of \(t .\) $$t=\frac{7 \pi}{6}$$

Find the period and graph the function. $$y=3 \csc \left(x+\frac{\pi}{2}\right)$$

Find the amplitude and period of the function, and sketch its graph. $$y=-3 \sin \pi x$$

Find the terminal point \(P(x, y)\) on the unit circle determined by the given value of \(t .\) $$t=-\frac{\pi}{3}$$

A Bobbing Cork A cork floating in a lake is bobbing in simple harmonic motion. Its displacement above the bottom of the lake is modeled by $$ y=0.2 \cos 20 \pi t+8 $$ where \(y\) is measured in meters and \(t\) is measured in minutes. (a) Find the frequency of the motion of the cork. (b) Sketch a graph of \(y .\) (c) Find the maximum displacement of the cork above the lake bottom.

Find the period and graph the function. $$y=\tan 4 x$$

Find the value of each of the six trigonometric functions (if it is defined) at the given real number \(t\). Use your answers to complete the table. $$t=\pi$$ (TABLE CAN'T COPY).

Find the amplitude and period of the function, and sketch its graph. $$y=1+\frac{1}{2} \cos \pi x$$