Hi I've been struggling with trigonometry for a while and I just don't get it, can you help me with finding the answer and explain how you got it. Thanks!

Question

Write the equation of the height of a rider on each of the following Ferris wheels t seconds after the rider passes the farthest right position'

The radius of the wheel is 20 feet, the center of the wheel is 30 feet above he ground, and the angular speed of the wheel is 14 degrees per second counterclockwise. Write the equation.

 

h(t) =  +  sin(  )

Answer 1

At t=0 the rider is level with the center of the wheel so if h(t) is the height above the ground at time t,

h(0) = 30

The height relative to the horizontal line going through the wheel center will be r sin Θ, where r = 20 and Θ is the angle of rotation from the horizontal counterclockwise at time t = 14t (from the question)

So the height at time t will be h(t) = 30 + 20 sin 14t

30 because h(0) = 30.

Answer 2

in these problems it is always very helpful to draw a picture

If the center of the wheel is 30 ft above the ground. The the midline for your graph ( vertical shift ) is 30 .

It the radius is 20 the the wheel will rise and fall this distance which the amplitude = 20

There is no phase shift

Lastly need to calculate the period. If the wheel travels at 14 degrees/ sec then period is the anount of time to complete one cycle or 360 degrees which is 360/14 = 25.7 seconds which I will round to 26 .

B= 2pi/P = 2pi/26 = pi/13 so equation is

y = 20sin( (pi/13)(t)+30