Exam 17: Graphs of the Trigonometric Functions

Graph $y=5 \sin \left(2 x-45^{\circ}\right)$ . Determine the amplitude, period, frequency, and phase shift.

Write the equation of a sine curve that has an amplitude of $\pi$ , a period of $\pi$ , and a phase shift of 0 .

Write the equation of a sine function that has an amplitude of 3 , a period of 2 , and a phase shift of 1 to the left.

Write the equation of a sine curve that has an amplitude of 6 , a period of $3 \pi$ , and a phase shift of $-2 \pi$ .

Graph the function $y=4 \csc (3 x+4)$ .

Express $y=13 \sin w t+17$ coswt as a single sine wave.

Graph the function $y=2 \cot (3 x+1)$ .

Graph $y=-3 \sin (3 x-6 \pi)$ . Determine the amplitude, period, and phase shift.

Plot the point $\left(3.5,15^{\circ}\right)$ , given in polar coordinates.

Transform the rectangular equation $x+3 y=4$ into polar form.

Rewrite $r=3$ in parametric form, and graph.

Write the rectangular equation $y=-5 x^{2}$ in polar form.

Write an equation for an alternating current that has a peak amplitude of $42.4 \mathrm{~mA}$ , a frequency of 35 $\mathrm{Hz}$ , and a phase angle of $42.1^{\circ}$ .

Transform the rectangular equation $x^{2}+y^{2}=16$ into polar form.

Graph the function $y=\sqrt{x}+\cos 2 x$ .

Express $(5.96,-8.23)$ in polar coordinates.

Find the period and angular velocity of a repeating waveform that has a frequency of $28 \mathrm{~Hz}$ .

Graph $y=\cos (\pi x+\pi)$ . Determine the amplitude, period, and phase shift.

Write an equation for an alternating voltage that has a peak value of $125 \mathrm{~V}$ , a frequency of $55 \mathrm{~Hz}$ , and a phase angle of $18.0^{\circ}$ .

Write polar coordinates of each point: (a) $(3.00,4.00)$ (b) $(2.00,5.00)$ (c) $(-5.00,-1.00)$ (d) $(-1.00,5.00)$