Mustafa 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)P(t)P, left parenthesis, t, right parenthesis (in \text{cm}cmstart text, c, m, end text) between the center of the tastiest looking slice and the door of the glass case as a function of time ttt (in seconds) can be modeled by a sinusoidal function of the form a\cdot\cos(b\cdot t)+da⋅cos(b⋅t)+da, dot, cosine, left parenthesis, b, dot, t, right parenthesis, plus, d.
At t=0t=0t, equals, 0, the center of the tastiest looking slice is farthest from the door, at a distance of 30\text{ cm}30 cm30, start text, space, c, m, end text away. After 2\pi2π2, pi seconds, it is closest to the door, at a distance of 10\text{ cm}10 cm10, start text, space, c, m, end text.
Find P(t)P(t)P, left parenthesis, t, right parenthesis.