options: Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.

Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.

Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
problem_activity: A Ferris wheel is 50 meters in diameter and rotates once every three minutes. The center axle of the Ferris wheel is 30 meters from the ground.
a. Using the axes below, sketch a graph to show how the height of a passenger will vary with time. Assume that when the wheel starts rotating when the passenger is at the bottom.
[IMG]
b. A mathematical model for this motion is given by the formula
$${h=a+b\mathrm{cos}ct}$$
where
$$h$$
= the height of the car in meters
$$t$$
= the time that has elapsed in minutes
$${a, b, c}$$
are constants
Find values for
$$a$$
,
$$b$$
, and
$$c$$
that will model this situation.


correct_option_index: 2