Unit 7, Lesson 5

The Pythagorean Identity (Part 1)

Algebra 2

Practice

Problem 1

Student Task Statement

The pictures show points on a unit circle labeled and . Which point is ?

Practice

A circle with center at the origin of an x y plane. Point B lies on the outside of the curve, in the first quadrant, and is closer to the y axis than the x axis.
A circle with center at the origin of an x y plane. Point B lies on the outside of the curve, in the fourth quadrant, and is closer to the x axis than the y axis.
A circle with center at the origin of an x y plane. Point D lies on the outside of the curve, in the fourth quadrant, and is closer to the y axis than the x axis.

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Problem 2

Student Task Statement

For which angles is cosine positive? Select all that apply.

0 radians
radians
radians
radians
radians

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Problem 3

Student Task Statement

Mark two angles on the unit circle whose measure satisfies . How do you know your angles are correct?

<p>Circle on a coordinate plane, center at the origin, radius 10 tick marks, no units given.</p>

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Problem 4

Student Task Statement

For which angle measures, , between 0 and radians is ? Label the corresponding points on the unit circle.
What are the values of for these angle measures?

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Problem 5

ForLesson 4: The Unit Circle (Part 2)

Student Task Statement

Angle measures radian, and the coordinates of are about .

<p>A circle on a coordinate plane, center at the origin, B, radius 1. Points on the circle, A, at 1 comma 0, C in the first quadrant, D in the second quadrant, E in the fourth quadrant. Segment B C.</p>

The measure of angle is radians. What are the approximate coordinates of ? Explain how you know.
The measure of angle is radians. What are the approximate coordinates of ? Explain how you know.

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Problem 6

ForLesson 4: The Unit Circle (Part 2)

Student Task Statement

In which quadrant is the value of the -coordinate of a point on the unit circle always greater than the -coordinate? Explain how you know.
Name 3 angles in this quadrant.

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Problem 7

ForLesson 3: More Movement

Student Task Statement

Lin is comparing the graph of two functions and . The function is given by . Lin thinks the graph of will be the same as the graph of , translated to the left by 2. Do you agree with Lin? Explain your reasoning.

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Problem 8

ForLesson 12: Transformation Effects

Student Task Statement

An original function is called . The function is transformed from using the following transformations, in this order:

Stretch horizontally by a factor of
Reflect over the -axis
Translate down 3

Write an equation for if is:

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The Pythagorean Identity (Part 1)

Practice

Problem 1

Student Task Statement

Problem 2

Student Task Statement

Problem 3

Student Task Statement

Problem 4

Student Task Statement

Problem 5

Student Task Statement

Problem 6

Student Task Statement

Problem 7

Student Task Statement

Problem 8

Student Task Statement

Lesson 5 Resources