91Ó°ÊÓ

Suppose that the terminal point determined by \(t\) is the point \(\left(\frac{3}{5}, \frac{4}{5}\right)\) on the unit circle. Find the terminal point determined by each of the following. (a) \(\pi-t\) (b) \(-t\) (c) \(\pi+t\) (d) \(2 \pi+t\)

The terminal point \(P(x, y)\) determined by a real number \(t\) is given. Find \(\sin t, \cos t,\) and \(\tan t\) $$\left(-\frac{6}{7}, \frac{\sqrt{13}}{7}\right)$$

Find the amplitude, period, and phase shift of the function, and graph one complete period. $$y=-4 \sin 2\left(x+\frac{\pi}{2}\right)$$

Find the period and graph the function. $$y=\csc 2 x$$

The terminal point \(P(x, y)\) determined by a real number \(t\) is given. Find \(\sin t, \cos t,\) and \(\tan t\) $$\left(\frac{40}{41}, \frac{9}{41}\right)$$

Find the amplitude, period, and phase shift of the function, and graph one complete period. $$y=\sin \frac{1}{2}\left(x+\frac{\pi}{4}\right)$$

Find the amplitude, period, and phase shift of the function, and graph one complete period. $$y=5 \cos \left(3 x-\frac{\pi}{4}\right)$$

Find the period and graph the function. $$y=2 \tan 3 \pi x$$

The terminal point \(P(x, y)\) determined by a real number \(t\) is given. Find \(\sin t, \cos t,\) and \(\tan t\) $$\left(-\frac{5}{13},-\frac{12}{13}\right)$$

A mass is suspended on a spring. The spring is compressed so that the mass is located \(5 \mathrm{cm}\) above its rest position. The mass is released at time \(t=0\) and allowed to oscillate. It is observed that the mass reaches its lowest point \(\frac{1}{2}\) s after it is released. Find an equation that describes the motion of the mass.