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Pythagorean Identities Worksheet

Grade 11 Math worksheet focusing on the application and verification of Pythagorean identities in trigonometry.

Grade 11 Math TrigonometryPythagorean Identities
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Includes

Fill in the BlanksMultiple ChoiceTrue / FalseShort AnswerCustom

Standards

CCSS.MATH.CONTENT.HSG.SRT.C.8CCSS.MATH.CONTENT.HSF.TF.C.8

Topics

MathTrigonometryPythagorean IdentitiesGrade 11
7 sections · Free to use · Printable
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Pythagorean Identities Practice

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Date:

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Read each question carefully and answer to the best of your ability. Show all your work for full credit.

1. The fundamental Pythagorean Identity states that sin²θ + cos²θ =  .

2. Dividing sin²θ + cos²θ = 1 by cos²θ gives the identity tan²θ + 1 =  .

3. Dividing sin²θ + cos²θ = 1 by sin²θ gives the identity 1 + cot²θ =  .

4. If sin(θ) = 3/5 and θ is in the first quadrant, what is cos(θ)?

a

4/5

b

5/4

c

3/4

d

1

5. Which of the following is equivalent to (1 - sin²θ) / cos²θ?

a

sin²θ

b

cos²θ

c

1

d

tan²θ

6. The identity 1 + tan²θ = sec²θ is derived from sin²θ + cos²θ = 1 by dividing by sin²θ.

T

True

F

False

7. If sec(θ) = 5/3, then tan(θ) must be 4/3.

T

True

F

False

8. Simplify the expression (sec²θ - 1) / tan²θ using Pythagorean identities.

9. Given that cot(θ) = -12/5 and θ is in the second quadrant, find the value of csc(θ).

10. Prove the identity: (1 - cos²x) / (1 - sin²x) = tan²x