Illustrative Math - Algebra 2 - Unit 6 - Lesson 18 - Formative Library | Library

The vertical position, in feet, of the point P on a windmill is represented by y=5sin(\frac{2\pi t}{3})+20, where t  is the number of seconds after the windmill started turning at a constant speed. 

Select all the true statements.

The windmill makes 3 revolutions per second.

The midline for the graph of the equation is 20.

The windmill blades are 5 feet long.

The windmill blades make 5 revolutions per second.

The windmill makes one revolution every 3 seconds.

F.IF.7.e

F.TF.5

F.IF.4

G.C.5

F.BF.1.a

F.TF.1

N.Q.1

A seat on a Ferris wheel travels 250\pi feet in one full revolution.

 How many feet is the carriage from the center of the Ferris wheel?

\frac{125}{\pi}

\frac{250}{\pi}

250

125

F.IF.7.e

F.TF.5

F.IF.4

G.C.5

F.BF.1.a

F.TF.1

N.Q.1

10.

11.

A \frac{\pi}{2} radian rotation takes a point D on the unit circle to a point E. Which other radian rotation also takes point D to point E?

\frac{3\pi}{2}

\frac{4\pi}{2}

\frac{5\pi}{2}

\frac{7\pi}{2}

F.IF.7.e

F.TF.5

F.IF.4

G.C.5

F.BF.1.a

F.TF.1

N.Q.1

12.

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

Which statements are true? Select all that apply.

The position of W  repeats every 10 seconds.

After \frac{1}{5} of a second, the point W  will be in its starting position.

In 1 second, the point W  travels through an angle of \frac{1}{5}.

The position of W  repeats every 5 seconds.

After 15 seconds, the point W  will be in its starting position.

F.IF.7.e

F.TF.5

F.IF.4

G.C.5

F.BF.1.a

F.TF.1

N.Q.1

13.

Here is the graph of a trigonometric function.
Which equation has this graph?

y=-2sin(2x)

y=2sin(2\pi(x-\frac{1}{4}))

y=2sin(2\pi(x+\frac{1}{4}))

y=2sin(2\pi(x+\frac{\pi}{4}))

F.IF.7.e

F.TF.5

F.IF.4

G.C.5

F.BF.1.a

F.TF.1

N.Q.1

This lesson is from Illustrative Mathematics. Algebra 1, Unit 6, Lesson 18. Internet. Available from https://curriculum.illustrativemathematics.org/HS/teachers/3/6/18/index.html ; accessed 29/July/2021.

IM Algebra 1, Geometry, Algebra 2 is © 2019 Illustrative Mathematics. Licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.

These materials include public domain images or openly licensed images that are copyrighted by their respective owners. Openly licensed images remain under the terms of their respective licenses. See the image attribution section for more information.