The Unit Circle (Part 1): IM Alg2.6.3
1. Alg2.6.3 Lesson
1. IM Alg2.6.3 Lesson: The Unit Circle (Part 1)
2. Alg2.6.3 Practice
1. IM Alg2.6.3 Practice: The Unit Circle (Part 1)

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The Unit Circle (Part 1): IM Alg2.6.3

GeoGebra Classroom Activities, Mar 22, 2021

[url=https://im.kendallhunt.com/HS/teachers/3/6/3/preparation.html]“The Unit Circle (Part 1)”[/url] from IM Algebra II © 2019 [url=https://www.illustrativemathematics.org/]Illustrative Mathematics[/url]. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0[/url] license.

Alg2.6.3 Lesson
1. IM Alg2.6.3 Lesson: The Unit Circle (Part 1)
Alg2.6.3 Practice
1. IM Alg2.6.3 Practice: The Unit Circle (Part 1)

1.

Alg2.6.3 Lesson

1. IM Alg2.6.3 Lesson: The Unit Circle (Part 1)

1.1.

IM Alg2.6.3 Lesson: The Unit Circle (Part 1)

The [math]x[/math]-coordinate of a point on the unit circle is [math]\frac{3}{5}[/math]. What does this tell you about where the point might lie on the unit circle? Find any possible [math]y[/math]-coordinates of the point and plot them on the unit circle.[br]

The [math]y[/math]-coordinate of a point on the unit circle is [math]-0.4[/math]. What does this tell you about where the point might lie on the unit circle? Find any possible [math]x[/math]-coordinates of the point and plot them on the unit circle.

All points are 1 unit from the origin.

Choose one of the points. Be prepared to describe its location using only words.

Your teacher will give you a circular object or you can use the applet below.

[list][*]About how many radii does it take to go halfway around the circle?[/*][*]About how many radii does it take to go all the way around the circle?[/*][*]Compare your answers to the previous two questions with your partners.[/*][/list]What is the exact number of radii that fit around the circumference of the circle? Explain how you know.

Why doesn’t the number of radii that fit around the circumference of a circle depend on the radius of the circle? Explain how you know.[br]

A bicycle wheel has a 1 foot radius. The wheel rolls to the left (counterclockwise).

What is the circumference of this wheel?[br]

Mark the point Q where P will be after the wheel has rolled 1 foot to the left. Be prepared to explain your reasoning.

Mark the point R where P will be after the wheel has rolled 3 feet to the left.

What angle, in radians, does [math]P[/math] rotate through to get to [math]R[/math]? Explain your reasoning.[br]

Where will point [math]P[/math] be after the bike has traveled [math]\pi[/math] feet to the left? What about [math]10\pi[/math] feet? [math]100\pi[/math] feet? Mark these points on the circle below. Explain your reasoning.[br]

After traveling some distance to the left, the point [math]P[/math] is at the lowest location in its rotation. How far might the bike have traveled? Explain your reasoning.[br]

[size=150]Picture the bicycle with a bright light at point [math]P[/math] and moving now from left to right. [br][/size]As the bike passes in front of you going left to right, what shape do you think the light would trace in the air?

2.

Alg2.6.3 Practice

1. IM Alg2.6.3 Practice: The Unit Circle (Part 1)

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The Unit Circle (Part 1): IM Alg2.6.3

Table of Contents

1.

Alg2.6.3 Lesson

1.1.

IM Alg2.6.3 Lesson: The Unit Circle (Part 1)

All points are 1 unit from the origin.

Your teacher will give you a circular object or you can use the applet below.

A bicycle wheel has a 1 foot radius. The wheel rolls to the left (counterclockwise).

Mark the point Q where P will be after the wheel has rolled 1 foot to the left. Be prepared to explain your reasoning.

Mark the point R where P will be after the wheel has rolled 3 feet to the left.

2.

Alg2.6.3 Practice

2.1.

IM Alg2.6.3 Practice: The Unit Circle (Part 1)

The table shows an angle measure in radians and the amount of rotation about a circle corresponding to the angle. For example, 2π radians corresponds to 1 full rotation. Complete the table.

Here are some points labeled on the unit circle:

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