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9-12 Integrated Math 3 Unit 6 Lesson 19

Gradeband

K-5 Math 6-8 Math •9-12 Math

Course

Integrated Math 1 Integrated Math 2 •Integrated Math 3

Unit

Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 •Unit 6 Unit 7

Modeling Prompts

Lesson

Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18 •Lesson 19 Lesson 20

K-5
6-8
9-12

Integrated Math 1
Integrated Math 2
Integrated Math 3

Algebra 1
Geometry
Algebra 2
Extra Support Materials for Algebra 1

Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7

Modeling Prompts

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Lesson 2
Lesson 3
Lesson 4
Lesson 5
Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson 10
Lesson 11
Lesson 12
Lesson 13
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Lesson 16
Lesson 17
Lesson 18
Lesson 19
Lesson 20

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Unit 6, Lesson 19

Modeling Circular Motion

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Integrated Math 3

Practice

Problem 1
Student Task Statement
Jada is riding on a Ferris wheel. Her vertical position, in feet, is modeled by the function , where is the number of minutes since she got on the ride.

How many minutes does it take the Ferris wheel to make one full revolution? Explain how you know.

What is the radius of the Ferris wheel? Explain how you know.

Sketch a graph of .

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Problem 2

Student Task Statement

The vertical position, in feet, of a point, , on a windmill is represented by , where is the number of seconds after the windmill started turning at a constant speed. Select all the true statements.

The windmill blades are 5 feet long.
The windmill blades make 5 revolutions per second.
The midline for the graph of the equation is 20.
The windmill makes one revolution every 3 seconds.
The windmill makes 3 revolutions per second.

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Problem 3

Student Task Statement

A seat on a Ferris wheel travels feet in one full revolution. How many feet is the carriage from the center of the Ferris wheel?

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Problem 4

Student Task Statement

A carousel has a radius of 20 feet. The carousel makes 8 complete revolutions.

How many feet does a person on the carousel travel during these 8 revolutions?
What angle does the carousel travel through?
What is the relationship between the angle of rotation and the distance traveled on this carousel? Explain your reasoning.

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Problem 5

ForLesson 6: The Pythagorean Identity (Part 2)

Student Task Statement

For which angle measures between 0 and is cosine negative and sine positive?
For which angle measures between 0 and is cosine negative and sine negative?

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Problem 6

ForLesson 10: Beyond

Student Task Statement

A -radian rotation takes a point, , on the unit circle to a point, . Which other radian rotation also takes point to point ?

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Problem 7

ForLesson 17: Features of Trigonometric Graphs (Part 2)

Student Task Statement

A windmill blade spins in a counterclockwise direction, making one full revolution every 5 seconds.

Which statements are true? Select all that apply.

<p>A windmill with 5 blades shaped like a tall trapezoid. On the outside end of one of the blade, in the center, a point labeled W.</p>

After 15 seconds, the point will be in its starting position.
After of a second, the point will be in its starting position.
In 1 second, the point travels through an angle of .
The position of repeats every 5 seconds.
The position of repeats every 10 seconds.

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Problem 8

ForLesson 18: Comparing Transformations

Student Task Statement

Here is the graph of a trigonometric function.

Which equation has this graph?

<p>graph of sine function shifted the fraction 1 over 4 to the right. period = 1. amplitude = 2. </p>

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Lesson 19 Resources

Student Materials

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