Prove that cycloid has this property and that circle doesn't

[Ardalan]

I need help proving that sin(θ)/√h is a constant in a cycloid and that it is not a constant in a circle.
I have defined h and θ in the image. θ is the angle between the vertical and the tangent line at a given point. h is the vertical distance from the beginning of the cycloid to the given point.
Thanks,
Ardalan

 

[Ardalan]

Using simplest math possible please.

 

[tkhunny]

1) You post in "Advanced Math" and include a plea to use the "simplest math possible"? Does that make sense to you?

2) I don't understand your definitions. Please try again.

 

[Dr.Peterson]

The simplest math possible will probably be calculus. Have you done any differentiation yet? Please show whatever you have done, so we can see where you need help. You have read this, right?

It will also be helpful to show the equations you are using for the circle and for the cycloid. So far, I don't even know whether you are using Cartesian coordinates or maybe a parametric equation.