Pythagorean Identities Worksheet
Grade 11 Math worksheet focusing on the application and verification of Pythagorean identities in trigonometry.
Includes
Standards
Topics
Pythagorean Identities Practice
Name:
Date:
Score:
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)?
4/5
5/4
3/4
1
5. Which of the following is equivalent to (1 - sin²θ) / cos²θ?
sin²θ
cos²θ
1
tan²θ
6. The identity 1 + tan²θ = sec²θ is derived from sin²θ + cos²θ = 1 by dividing by sin²θ.
True
False
7. If sec(θ) = 5/3, then tan(θ) must be 4/3.
True
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