Illustrative Mathematics | v.360 Curriculum

Problem 1

Student Task Statement

A rotation takes to . What could be the measure of the angle of rotation in radians? Select all that apply.

<p>Circle on an x y axis. Point P is on the circle on the positive x axis. Point Q is on the circle on the positive y axis.</p>

to access Practice Problem Solutions.

Problem 2

Student Task Statement

A radian rotation takes to . Label .
A radian rotation takes to . Label .
A radian rotation takes to . Label .

<p>Circle on an x y axis. Point N on the circle on the positive x axis.</p>

Problem 3

Student Task Statement

Here is a wheel with a radius of 1 foot.

<p>A circle with center at the origin of an x y plane. </p>

List three different counterclockwise angles the wheel can rotate so that point ends up at position .
How many feet does the wheel roll for each of these angles?

Problem 4

Student Task Statement

A point on the unit circle is in the 0 radian position.

Which counterclockwise rotations take back to itself? Explain how you know.
Which counterclockwise rotations take to the opposite point on the unit circle? Explain how you know.

Problem 5

ForLesson 4: The Unit Circle (Part 2)

Student Task Statement

Here is the unit circle with a point at . Find the coordinates of after the circle rotates the given amount counterclockwise around its center.

<p>A circle with center O at the origin of an x y plane. Point P lies on the outside of the circle, on the x axis, to the right of the origin.</p>

of a full rotation
of a full rotation
of a full rotation

Problem 6

ForLesson 9: Introduction to Trigonometric Functions

Student Task Statement

Here is a graph of .

Plot the points on the graph where .
For which angles does ?

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Problem 1

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Problem 2

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Problem 3

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Problem 4

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Problem 5

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Problem 6

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Lesson 10 Resources