The full question: A point on a wheel has an equation y = 10 sin (x - 45°) + 20 that models the height as the wheel rotates. Answer the following questions.

Question

1) What is the height if the wheel has rotated 135°?

2) What are the possible values of rotation (i.e., the value of x) if the height is 15m?

3) If the hub of the wheel were moved down 5m, what would the values of rotation (the values of x) be if the height were 15m?

I've answered 1 just fine on my own, and this is what I have for 2 so far:

y=10sin(x-45°)+20
15-20=10sin(x-45°)+20
-5/10=10sin(x-45°)/10
-0.5=sin(x-45°)

I'm having trouble figuring out how to remove the 45° from the equation. I looked at the examples in the lesson, but it doesn't include an example involving the phase shift, and I'm just confused. I did a bit of Googling out of frustration and found the answers are supposed to be 210° and 330°, but I don't know how to get to those answers. If anyone could point me in the right direction, I'd be super grateful.

Answer 1

y=10sin(x-45°)+20 y is the height, so
15-20=10sin(x-45)
sin(x-45)= -.5
sinTheta= -.5
theta= 330deg, or 210
but x-45=210, or 330 so
x= 255 or 375 (15 deg)