91Ó°ÊÓ

Graph each function in polar coordinates. $$r=3 \sin \theta+3$$

Graph each sine wave. Find the amplitude, period, and phase shift.$$y=\sin \left(2 x+55^{\circ}\right)$$

Graph each function in polar coordinates. $$r=2 \cos \theta-1$$

Make a complete graph of each function. $$y=4 \tan \left(x+\frac{\pi}{6}\right)$$

Plot each sine wave. $$y=\sin t$$

Graph each sine wave. Find the amplitude, period, and phase shift.$$y=\sin \left(3 x-25^{\circ}\right)$$

Trajectories: If air resistance is neglected, a projectile will move horizontally with constant velocity and fall with constant acceleration like any falling body. Thus if the projectile is launched with an initial horizontal velocity of \(453 \mathrm{ft} / \mathrm{s}\) and an initial vertical velocity of \(593 \mathrm{ft} / \mathrm{s}\), the parametric equations of motion will be: $$ x=453 t \mathrm{ft} \quad \text { and } \quad y=593 t-16.1 t^{2} \mathrm{ft} $$ (a) Graph these equations to get the trajectory of the projectile. From the graph, determine (b) the projectile's maximum height. (c) the \(x\) distance for which the height is a maximum. (d) the projectile's maximum distance, assuming that the ground is level. (e) the height when \(x=5000 \mathrm{ft}\)

Plot each sine wave. $$y=3 \sin 377 t$$

Graph each function in polar coordinates. $$r=3 \cos 2 \theta$$

Graph each sine wave. Find the amplitude, period, and phase shift.$$y=\sin (3 x-\pi / 3)$$