options: Build new functions from existing functions.

Use functions to model relationships between quantities.

Construct and compare linear and exponential models and solve problems.

Extend the domain of trigonometric functions using the unit circle.

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

Analyze functions using different representations.

Build a function that models a relationship between two quantities.

Prove and apply trigonometric identities.

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

Model periodic phenomena with trigonometric functions.

Define, evaluate, and compare functions.

Understand the concept of a function and use function notation.
problem_activity: Warm-up
The purpose of this warm-up is to prepare students for “unwrapping” the unit circle in the next activity and seeing what the graphs of
\(y=\cos(x)\)
and
\(y=\sin(x)\)
look like for the first time in this unit. Part of thinking of cosine and sine as functions is understanding their input and output. The prompts in this activity ask students to informally describe the output of the two trigonometric functions by focusing on each coordinate of a point on the unit circle.
Launch
Display the image for all to see.
Student Facing
Suppose there is a point
\(P\)
on the unit circle at
\((1,0)\)
.
[IMG]
Describe how the
\(x\)
-coordinate of
\(P\)
changes as it rotates once counterclockwise around the circle.
Describe how the
\(y\)
-coordinate of
\(P\)
changes as it rotates once counterclockwise around the circle.
Student Response
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Activity Synthesis
Invite students to share their descriptions, highlighting responses that use actual values such as 1, 0, and -1.


correct_option_index: 3