Given:
D=165 feet and the frequency of the motion is 1.6 revolutions per minute.
Solution:
The radius is half of the diameter.
The radius of the wheel is 82.5 feet.
As we know: 
Substitute the value of T in the above formula.
If the center of the wheel is at the origin then for 
the rest position is 
.
This can be written as:
The actual height of the rider from the ground is:
The required equation is 
.
When we use arcsine, we are finding the angle while giving the trigonometric ratio.
Arcsin(u) = theta can be rewritten as:
sin(theta) = u
Sine is opposite over hypotenuse, so u/1 means that the side opposite to theta (the y value) is u, and the hypotenuse is 1.
We can use Pythagorean Theorem to find the adjacent (x value).
1^2 - u^2 = x^2
x = sqrt(1-u^2)
Back to the original question, we are trying to find cos(arcsin(u)). We just solved all the sides for our triangle using arcsin(u). Now we need to do cos(u).
Cosine is adjacent over hypotenuse.
So our answer is sqrt(1-u^2)/1
Or just sqrt(1-u^2)
Note: Let us consider, we need to find the 
and 
.
Given:
In the given figure, BD is the angle bisector of ABC.
To find:
The and .
Solution:
BD is the angle bisector of ABC. So,
Divide both sides by 2.
Now,
And,
Therefore, 
and .
