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Unit 6, Lesson 6

The Pythagorean Identity (Part 2)

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Integrated Math 3

Practice

Problem 1
Student Task Statement

The picture shows angles and . Explain why and why .

Practice

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Problem 2

Student Task Statement

Which statements are true? Select all that apply.

for an angle in Quadrant II
for an angle in Quadrant II
for an angle in Quadrant II
for an angle in Quadrant III
for an angle in Quadrant III
for an angle in Quadrant III

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Problem 3

Student Task Statement

The tangent of an angle satisfies .

Which quadrant could lie in? Explain how you know.
Estimate the possible value(s) of . Explain your reasoning.

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Problem 4

Student Task Statement

Evaluate each of the following:

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Problem 5

Student Task Statement

The sine of an angle, , in the second quadrant is . What is ? Explain how you know.

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Problem 6

ForLesson 5: The Pythagorean Identity (Part 1)

Student Task Statement

Triangle is an isosceles right triangle in the unit circle.

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

Explain why .
Use the Pythagorean Identity to explain why .

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Problem 7

ForLesson 2: Revisiting Right Triangles

Student Task Statement

Triangle is similar to triangle . The scale factor going from triangle to triangle is 3.

<p>Two triangles. First, A, B C with B is a right angle. Second, D E F, E is a right angle.</p>

Explain why the length of segment is 3 times the length of segment and the length of segment is 3 times the length of segment .
Explain why .

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Problem 8

ForLesson 5: The Pythagorean Identity (Part 1)

Student Task Statement

Which of the following is true for angle ? Select all that apply.

<p>A circle with radius 1 inscribed on a coordinate plane, centered at the origin. Point P is on the circle in the third quadrant. Sector is labeled theta.</p>

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The Pythagorean Identity (Part 2)

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 6 Resources