Question

A ferris wheel is 28 meters in diameter and makes one revolution every 10 minutes. For how many minutes of any revolution will your seat be above 21 meters?

Answer 1

fit your data into a sine curve
period of sine curve = 10 minutes
2π/k = 10
k = 2π/10 = π/5
so start with
y = 14 sin π/5 t + 14

testing:
t = 0: y = 14sin0 + 14 = 14
t = 2.5 , y = 28
t = 5 , y = 14
t = 7.5 , y = 0
t = 10 , y = 14 , looks good

solve for
14 sin πt/5 + 14 = 21
sin πt/5 = 1/2
πt/5 = π/6 or πt/5 = 5π/6
t = 5/6 or t = 25/6 minutes

so time over 21 metres = 25/6 - 5/6 = 20/6 minutes
or 2 minutes and 20 seconds or 200 seconds

Answer 2

I'm sure the answer is unchanged, but I'd have set up the equation as

y = 14(1 - cos pi/5 t)

That way, y(0) = 0, when the person gets on the wheel, rising to y(5) = 28 when it's 5 minutes later, at the top. And so on.