A Ferris Wheel Model

Part of the Graphs of Trig Functions section of Coddy's Trigonometry journey. Lesson 40 of 51.

A Ferris wheel has radius 10 m and its hub is 12 m above the ground. You board at the bottom, 2 m up. After the wheel turns x degrees you are 10cos(x) metres below the hub (a negative number once you are above it), so your height is

h = 12 - 10cos(x)

$Height on a wheel of radius 10 with its hub 12 m up: from 2 m at 0 degrees to 22 m at 180 degrees$

Read the model like any wave: the midline is the hub, the amplitude is the radius, and the period is one turn, 360°. A ride that starts at the bottom is a cosine with a negative a. One that starts level with the hub on the way up would be a sine instead.

Challenge

A Ferris wheel has radius 18 m and its hub is 20 m above the ground. You board at the bottom. Draw your height above the ground in metres against the angle x the wheel has turned, in degrees. Press Check.