Open main menu

Wikibooks β

Trigonometry/Worked Example: Ferris Wheel Problem

< Trigonometry

A ferris wheel with a radius of 15m and starts half way the highest point on the right. Find the y coordinate and x coordinate after going through 56 degrees?


The ProblemEdit

Exam QuestionEdit

"Jacob and Emily ride a Ferris wheel at a carnival in Vienna. The wheel has a 16 meter diameter, and turns at three revolutions per minute, with its lowest point one meter above the ground. Assume that Jacob and Emily's height h above the ground is a sinusoidal function of time t, where t=0 represents the lowest point on the wheel and t is measured in seconds."

"Write the equation for h in terms of t."

[For those interested the picture is actually of a Ferris wheel in Vienna.]

-Lang Gang 2016

Video LinksEdit

The Khan Academy has video material that walks through this problem, which you may find easier to follow:


Diameter to Radius

A 16m diameter circle has a radius of 8m.

Revolutions per Minute to Degrees per Second

A wheel turning at three revolutions per minute is turning


per second. Simplifying that's


per second.

Formula for height

At t=0 our height h is 1. At t =10 we will have turned through 180o, i.e. half a circle and will be at the top most point which has height 16 + 1= 17.

A cosine function, i.e.   is 1 at   and -1 at  . That's almost exactly opposite to what we want as we want the most negative value at 0 and the most positive at 180. So let's start with negative cosine as our function.

At t=10 we want  , so we will take  . That's -1 at t=0 and +1 at t=10. Multiply by 8 and we get:

 . That's -8 at t=0 and +8 at t=10

Add 9 and we get

 . Which is 1 at t=0 and +17 at t=10

Our required formula is


with the understanding that cosine is of an angle in degrees (not radians).