# Math Help - equations of circles trig

1. ## equations of circles trig

I need to know how to solve a problem like this on my final tomorrow and I don't know how, please help!

So there's a ferris wheel. The bottom is say 5 feet off the ground. It has a radius of 10 feet. It turns 1 degree every second.

How would I write this wheel's equation?? like how to find the height for time "t"

I don't even know where to start...

2. Hello, pyrosilver!

So there's a ferris wheel. The bottom is say 5 feet off the ground.
It has a radius of 10 feet. It turns 1 degree every second.
There is no "wheel's equation".

But we can express the height of a "car" at time $t.$
Code:
              * * *
*           *
*               *
*                 *

*         O         *
*         *         *
*   10  *t|         *
*   |
*  *     |        *
A * - - - *B      *
: *     |     *
:     * * *
h :      C|
:       | 5
:       |
- - - * - - - * - - - - - -
E       D

The center of the wheel is at $O.$
Its radius is: $OA = OC = 10.$
"The bottom is 5 feet off the ground": $CD = 5,\;OD = 15$

The car is at $A.$
Since the wheel turns 1 degree per second,
. . in $t$ seconds, radius $OA$ has moved $t$ degrees: . $\angle AOB = t$

The height of the car is: $h \:=\:AE \:=\:BD.$

In right triangle $OBA\!:\;\;\cos t \:=\:\frac{OB}{10} \quad\Rightarrow\quad OB \:=\:10\cos t$

Then: . $BD \:=\:OD - OB \:=\:15 - 10\cos t$

. . Therefore: . $h \;=\;15 - 10\cos t$

3. Thank you so much...I totally get this now. Thank you SO MUCH! You are amazing!