Dr. Evil wants to strap your head, feet, hands and waist in a starfish shape onto a wheel so that your mouth is right at the same level as the rim. Your waist is belted onto the center point of the wheel and as the wheel turns your head will end up dunked underwater. (Dr. Evil truly is evil.)

The wheel Dr. Evil invented has a customizable radius to fit you specifically. The motor that spins the wheel is set up so that your head spends exactly 1 minute and 45 seconds under the water in a single revolution (Dr. Evil knows that the average person can hold their breath for about 2 minutes underwater, so he’s not completely evil.) When you’re initially put onto the machine, your head is perpendicularly above the line of the water level.

This should include
*A picture (sketch, diagram, etc, be creative!) of the situation
*your wheel’s radius
*the height above the water of the center of your wheel.

Your sine or cosine model to describe the height (in feet) of your head above (or below!) the water in terms of time (in seconds). Consider your head to be a single point on the rim of the wheel
A description of how you developed your equation, Include amplitude, period, any shifts, and the equation.
A graph your model for t 0 and at least 2 cycles.
LABEL your graph
DEFINE your variables
Include a SCALE
Your model should be digitally generated (Desmos!)
A description and rationale of a reasonable domain for your graph in the context of the problem.
A discussion of what times your head will go into and then out of the water in the first two cycles. Try to complete this work algebraically first and then support your work with the use of technology.