Chapter 15

Plot each point in polar coordinates. $$\left(4,35^{\circ}\right)$$

Graph the following parametric equations for values of \(t\) from -3 to 3 $$x=t, y=t$$

Find the period and the angular velocity of a repeating waveform that has a frequency of $$68.0 \mathrm{Hz}$$

Graph each sine wave. Find the amplitude, period, and phase shift.$$y=2 \sin x$$

Make a complete graph of each function. Find the amplitude, period, and phase shift. $$y=3 \cos x$$

Plot each point in polar coordinates. $$\left(3,120^{\circ}\right)$$

Graph the following parametric equations for values of \(t\) from -3 to 3 $$x=3 t, y=t^{2}$$

Find the period and the angular velocity of a repeating waveform that has a frequency of $$10.0 \mathrm{Hz}$$

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

Make a complete graph of each function. Find the amplitude, period, and phase shift. $$y=-2 \cos x$$

Writing the Equation, Given \(a\), the Period, and the Phase Shift Write the equation of a sine curve with \(a=3,\) a period of \(4 \pi,\) and a phase shift of zero.

Plot each point in polar coordinates. $$\left(2.5,215^{\circ}\right)$$

Graph the following parametric equations for values of \(t\) from -3 to 3 $$x=-t, y=2 t^{2}$$

Find the period and the angular velocity of a repeating waveform that has a frequency of $$5000 \mathrm{Hz}$$

Graph each sine wave. Find the amplitude, period, and phase shift.$$y=\sin 2 x$$

Writing the Equation, Given \(a\), the Period, and the Phase Shift Write the equation of a sine curve with \(a=-2,\) a period of \(6 \pi,\) and a phase shift of \(-\pi / 4\)

Make a complete graph of each function. Find the amplitude, period, and phase shift. $$y=\cos 3 x$$

Plot each point in polar coordinates. $$\left(3.8,345^{\circ}\right)$$

Graph the following parametric equations for values of \(t\) from -3 to 3 $$x=-2 t, y=t^{2}+1$$

Find the frequency (in hertz) and the angular velocity of a repeating waveform whose period is $$1.00 \mathrm{s}$$.

Make a complete graph of each function. Find the amplitude, period, and phase shift. $$y=\cos 2 x$$

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

Plot each point in polar coordinates. $$\left(2.7, \frac{\pi}{6}\right)$$

Graph each pair of parametric equations. $$\begin{aligned} &x=\sin \theta\\\ &y=\sin \theta \end{aligned}$$

Find the frequency (in hertz) and the angular velocity of a repeating waveform whose period is $$\frac{1}{8} \mathrm{S}$$.

Project, Composite Curves, Addition of Ordinates: One way to graph a function containing several terms is to graph each term separately and then add (or subtract) them on the graph paper. This method, called the method of addition of ordinates, is especially useful when one or more terms of the expression to be graphed are trigonometric functions. Graph the curve \(y=8 / x+\cos x\) by separately graphing \(y=8 / x\) and \(y=\cos x,\) and graphically adding the ordinates of each to obtain the final curve. Here \(x\) is in radians.

Make a complete graph of each function. Find the amplitude, period, and phase shift. $$y=2 \cos 3 x$$

Graph each sine wave. Find the amplitude, period, and phase shift.$$y=3 \sin 2 x$$

Plot each point in polar coordinates. $$\left(3.9, \frac{7 \pi}{8}\right)$$

Find the frequency (in hertz) and the angular velocity of a repeating waveform whose period is $$95.0 \mathrm{ms}$$

Graph each pair of parametric equations. $$\begin{aligned} &x=\sin \theta\\\ &y=2 \sin \theta \end{aligned}$$

Make a complete graph of each function. Find the amplitude, period, and phase shift. $$y=3 \cos 2 x$$

Graph each sine wave. Find the amplitude, period, and phase shift.$$y=2 \sin 3 x$$

Plot each point in polar coordinates. $$\left(-3, \frac{\pi}{2}\right)$$

Find the frequency (in hertz) and the angular velocity of a repeating waveform whose period is If a periodic waveform has a frequency of \(60.0 \mathrm{Hz}\), how many seconds will it take to complete 200 cycles?

Make a complete graph of each function. Find the amplitude, period, and phase shift. $$y=\cos (x-1)$$

Graph each pair of parametric equations. $$\begin{aligned} &x=\sin \theta\\\ &y=\sin 2 \theta \end{aligned}$$

Graph each sine wave. Find the amplitude, period, and phase shift.$$y=\sin \left(x+15^{\circ}\right)$$

Plot each point in polar coordinates. $$\left(4.2, \frac{2 \pi}{5}\right)$$

Make a complete graph of each function. Find the amplitude, period, and phase shift. $$y=\cos (x+2)$$

Graph each pair of parametric equations. $$\begin{aligned} &x=\sin \theta\\\ &y=\sin 3 \theta \end{aligned}$$

Graph each sine wave. Find the amplitude, period, and phase shift.$$y=\sin \left(x-45^{\circ}\right)$$

Plot each point in polar coordinates. $$\left(3.6,-20^{\circ}\right)$$

Find the period and the frequency of a sine wave that has an angular velocity of $$455 \mathrm{rad} / \mathrm{s}$$

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

Graph each pair of parametric equations. $$\begin{array}{l} x=\sin \theta \\ y=\sin (\theta+\pi / 4) \end{array}$$

Graph each sine wave. Find the amplitude, period, and phase shift.$$y=\sin (x-\pi / 2)$$

Find the period and the frequency of a sine wave that has an angular velocity of $$2.58 \mathrm{rad} / \mathrm{s}$$

Make a complete graph of each function. Find the amplitude, period, and phase shift. $$y=2 \cos (3 x+1)$$

Graph each pair of parametric equations. $$\begin{array}{l} x=\sin \theta \\ y=\sin (2 \theta-\pi / 6) \end{array}$$