Question

The paddle wheel of a boat measures 16 feet in diameter and is revolving at a rate of 20 rpm. The maximum depth of the paddle wheel under water is 1 foot. Suppose a point is located at the lowest point of the wheel at t=0.

1) Write a cosine function with phase shift 0 for the height above water at the initial point after t seconds

2) use your function to find the height of the initial point after 5.5 seconds

3) and find the values of x for which the equation sin x= -1 is true.

Thanks for any assistance

Answer 1

w = angular rate = 20*2pi/60 = 2pi/3 radians/sec
r = 16/2 = 8 feet
height of point above axle of wheel = -8cos wt
height of point above water = h = 7 - 8 cos wt
since w = 2 pi/3
h = 7 - 8 cos (2 pi t /3)
if t = 5.5
h = 7 - 8 cos (11 pi/3)
= -.839 ft
I do not understand what 3) has to do with this.
sin anything is -1 for 3pi/2, 3pi/2 + n*2pi