The equation below gives the height h of a passenger on a Ferris wheel at any time t during the ride to be
h = 137 − 122 cos (π/10)t
where h is given in feet and t is given in minutes. Use this equation to find the times at which a passenger will be 120 feet above the ground during the first revolution.

I found the first time, which is about 4.5, but I'm confused on how to find the second time.

Question

The equation below gives the height h of a passenger on a Ferris wheel at any time t during the ride to be
h = 137 − 122 cos (π/10)t
where h is given in feet and t is given in minutes. Use this equation to find the times at which a passenger will be 120 feet above the ground during the first revolution. 

I found the first time, which is about 4.5, but I'm confused on how to find the second time.

anonymous · Answer

are you familiar with the unit circle?

the are 2 quadrants in the unit circle which cos(t) is positive

itsonlycdeee · Answer

Yes, the 1st quadrant and the 4th quadrant.

anonymous · Answer

is t inside or outside of the cos?

itsonlycdeee · Answer

Outside

primeralph · Answer

Should be inside.

primeralph · Answer

Well, most likely.

anonymous · Answer

are you sure?,
because then h = 137 − 122 cos (π/10)t would be linear,

meaning there is only 1 time h = 120

itsonlycdeee · Answer

Oh, then inside does make more sense.

anonymous · Answer

120 = 137 − 122 cos (π/10*t)

-17 = -112 cos(π/10*t)

17/112  = cos(pi/10*t)

$$\cos^{-1} (17/112) = \frac{ \pi }{ 10 }t$$

itsonlycdeee · Answer

Thank you I just figured it out!