Graph the equation to show one rotation of a Ferris Wheel

Question

The equation h(t)=30cos π/10+50 has three parts in my book yet I don’t know where to begin!

A: graph the equation to show one complete rotation and label the Period, Midline and Amplitude

B: What is the diameter

C: What is the height of the rider after 18 seconds

Answer 1

You may have left out "t" in the equation's right side

h(t)=30cos(pi/10) + 50

maybe you meant to include it as follows, as a multiple of pi/10,

h(t)=30cos([(pi/10)t] + 50

when t = 0 the cosi(0) = 1 and h=80

that is the maximum height. The minimum height would be when cosine = -1 and h=20. That happens when pi/10(t) = pi or t=10 seconds

From t=0 to t= 10 seconds is half a rotation. A full rotation would then take 20 seconds. 30 the amplitude of the cosine graph. The amplitude is the distance from midline to the maximum or 80-50=30. A normal cosine graph has period 2pi, where it begins repeating, the period from maximum to maximum. 2pi would have been the period if the pi/10 were not the coefficient of t. But pi/10(t) = 2pi

t/10 = 2

or t=20 seconds = the period

It takes 20 seconds to go from height 80, down to 20, then back to 80, the maximum height. It's at a maximum height at t=0 and t=20, and other integer multiples of 20, t=40, t=60, ...

The midline or middle of the h graph is h=50, the mean height

After 20 seconds the height is at a maximum, 80, 80-50=30=amplitude

After 18 seconds, it's almost 80 but h<80

Just plug 18 into the equation

h(18) = 30cos[(pi/10)(18)] + 50

=30cos(9pi/5) + 50

=30(0.995) + 50

=29.894 + 50

h=79.894 which is almost the maximum 80

Subtract maximum from minimum height , 80-20 = 60 = the diameter

the diameter is 2 times the amplitude, or 2x30=60

This all assumes putting the "t" inside the cosine, as a multiple of pi/10