Question

A man is staring at a pizza spinning on a wheel in a glass case.

The pizza is cut into four even slices. The distance P(t) (in cm) between the center of the tastiest looking slice and the door of the glass case can be modeled by a sinusoidal function of the form: a*cos(b*t) + d.

At t=0, the center of the tastiest looking slice is farthest from the door, at a distance of 30 cm away. After 2π seconds, it is closest to the door, at a distance of 10 cm.

Find P(t) where t should be in radians.

Answer 1

Okay.
How do we determine the period?
How do we determine the average displacement?
How do we determine the amplitude?

Answer 2

2pi/b=period
this is what I know but how to get b?

Answer 3

You must extract the information from the given information.
At t=0, the center of the tastiest looking slice is farthest from the door
After 2π seconds, it is closest to the door

Do you see it?

Answer 4

so the period is 4 times 2pi.

Answer 5

2* 2pi. We are told that 2pi is half the period.

Answer 6

Ok. so the period is 4 pi
then to get the amplitude: 30 - 10 ?

Answer 7

No. Half of that. The amplitude of f(x) = cos(x) is 1, not 2.

Answer 8

Can you illustrate with a figure or something, writing is not enough.
Let me get the idea please.