Exam 17: Graphs of the Trigonometric Functions

Write the polar equation $r=25$ in rectangular form.

Graph the equation $r=\sin \theta+1$ , given in polar coordinates.

Express $y=21.5 \sin w t+22.5 \sin \left(w t+30.0^{\circ}\right)$ as a single sine wave.

Graph the equation $r=2+2 \cos \theta$ , given in polar coordinates.

Graph $y=12 \sin x$ . Determine the amplitude and period.

Express $(2.50,-3.20)$ in polar coordinates.

Graph $y=-12 \sin 4 x$ . Determine the amplitude, period, and phase shift.

Find the period and angular velocity of a repeating waveform that has a frequency of $72 \mathrm{~Hz}$ .

Express $y=74.1 \sin w t+85.2 \cos w t$ as a single sine wave.

Graph the function $y=\sin 2 x+\cos x$ .

Write the polar equation $r=4 \sin \theta+3 \cos \theta$ in rectangular form.

Graph the function $y=3 \tan 5 x$ .

Graph $y=0.2 \sin 3 \pi x$ . Determine the amplitude, period, frequency, and phase shift.

Plot the point $\left(6,-205^{\circ}\right)$ , given in polar coordinates.

Determine the period, frequency, and amplitude for this periodic waveform:

Write the equation of a sine curve that has an amplitude of 10 , a period of $5 \pi$ , and a phase shift of $\pi / 2$ .

Graph $y=5 \sin 2 x$ . Determine the amplitude, period, and phase shift.

Graph $y=\sin \left(x-\frac{3 \pi}{2}\right)$ . Determine the amplitude, period, frequency, and phase shift.

Transform the polar equation $r=3 \sin \theta$ into rectangular form.

Graph the function $y=\sin x+\cos 3 x$ .