## Sinusoidal Function

A bug has landed on the rim of a jelly jar and is moving around the rim. The location where the bug initially lands is described and its angular speed is given. Impose a coordinate system with the origin at the center of the circle of motion. For each of the scenarios below, answer the two questions.

Both coordinates of
P(t) = (x(t), y(t)) are sinusoidal functions in the variable t. Sketch a rough graph of the functions
x(t)
and y(t)
on the domain 0≤ t ≤ 11

x(t):

y(t):

Use the graph sketches to help you find the the amplitude, mean, period and phase shift for each function. Write x(t)
and y(t)
in standard sinusoidal form. (Round phase shifts to four decimal places.)

x(t)
Amplitude: 2
Mean: 0
Period: 5.5
Phase Shift: -2.337
y(t)
Amplitude: 2
Mean: 0
Period: 5.5
Phase Shift: -0.9629

I am having a hard time figuring out how to get these phase shift numbers...can someone explain how to get them? I understand how to get the rest, it is just that the phase shifts I don't understand. Thank you!