A water wheel with radius 2m has 0.2m submerged and rotates at 5 rev/min. (assume the wheel enters the water at t=0).

Write a sine function describing the hieght above the water taking the opint at which the wheel touches the water at t=0.

My solution:

The equation is of the form:

y=2sin(10pi x)+1.8

Find Phase shift using substitution (let p represent the phase shift)

(0,0) is a point on the function so it satisfies the equation.

0=2sin(10pi(0-p)+1.8

0=2sin(-10pi p)+1.8(since sin(-x) = -sin(x) where the (x) is the (-10pi p), although i might have went wrong here..)

-1.8=-2sin(10pi p)

0.9 = sin(10pi p)

10pi p=1.12 (first quadrant), 10pi p = 2.02 (second quadrant)

p = 0.036, p = 0.064

but then when u blug both of these phase shifts into the original equation to get

y=2sin(10pi(x-0.036))+1.8

and y=2sin(10pi(x-0.064))+1.8

those two functions aren't the same when you graph them.. the reference answer says the second one is right. WHY..?!?!

I bolded where I think I went wrong.. can someone please explain this to me?