standard_description: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
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.


aligns: no