How can I write a function for this ferris wheel problem? *ASAP*

Question

A Ferris wheel has a diameter of 12 meters and makes one complete revolution every 12

seconds. The bottom of the wheel is 2 meters above the ground. Jonah starts his stopwatch when

his car is 5 meters off the ground and the wheel starts to rotate upward. Write a function for his

height, h, off the ground in terms of time, t. Then use your function and technology to find the

second time Jonah is 11 meters off the ground.

Answer 1

The height he is off the ground is correlated to the sin function. We know that the center of the ferris wheel is at 8 meters off the ground (clearance at the bottom [2 m] plus half the diameter [6 m]). Thus the height at any given time is h=6sin(θ)+8. Now we need a function for θ. If the bottom of the ferris wheel at time 0, it rotates 360°/12 seconds, and the bottom of the ferris wheel is at 270°, then θ=30t+270, where θ is measured in degrees and t is in seconds. But he didnt start his watch until he was 5 meters off the ground which is at 330°, so actually θ=30t+330

Thus the final equation is h=6*sin(30*t+330)+8

He would reach 11 meters the first time when θ=30° and t is 2 sec, the second time would be when θ=150° and t is 6 seconds.