options: Use functions to model relationships between quantities.

Construct and compare linear and exponential models and solve problems.

Analyze functions using different representations.

Model periodic phenomena with trigonometric functions.

Define, evaluate, and compare functions.

Understand the concept of a function and use function notation.

Build new functions from existing functions.

Extend the domain of trigonometric functions using the unit circle.

Build a function that models a relationship between two quantities.

Interpret expressions for functions in terms of the situation they model.

Interpret functions that arise in applications in terms of the context.

Prove and apply trigonometric identities.
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: 3

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