Precalculus Trigonometry Question

Question

The Giant Sky Wheel is a Ferris wheel in Tokyo with a diameter of 100 meters that completes one full revolution every 16 minutes.¹ A rider boards at the bottom of the Ferris wheel which is 15 meters above the ground and rides for 32 minutes.



(a) Graph of the height, h, of the rider as a function of the time, t, after the rider boards the Ferris wheel. Use your graph to estimate the times during the first half hour of the ride at which the rider is 100 meters above the ground.

First time ≈  _minutes.

Second time ≈ _minutes.

Third time ≈ _minutes.

Fourth time ≈ _minutes.

(b) Find, to the nearest second, the times during the first half hour of the ride at which the rider is 100 meters above the ground.

First time = _seconds and _minutes

Second time = _seconds and _minutes

Third time =_seconds and _minutes

Fourth time = _seconds and _minutes

Answer 1

so lets take this question piece by piece, you start 15m above the ground, the radius of the wheel is 50m, and it takes 16min to do a full revolution, so lets find the pieces of the equation:

Amplitude=50 for the radius of the wheel

Period:2pi/16=pi/8

Vertical Shift: 65, (15+50)

Trig Function: -Cos(x) (start at the bottom/ min which is a cos function)

Now lets build the function:

y=-50cos(pi*x/8)+65

you will need to graph the function on your own to solve for a. To solve for b plug in 100 for y and solve for x:

100=-50cos(pi*x/8)+65, 35=-50cos(pi*x/8), -5/8=cos(pi*x/8), pi*x/8=cos^-1(-5/8),x=8cos^-1(-5/8)/pi, now find all the values for x that are between 0 and 32