Grade 12 Pythagorean Identities Worksheet
A Grade 12 mathematics worksheet focusing on understanding and applying Pythagorean Identities in trigonometric equations and proofs.
Includes
Standards
Topics
Pythagorean Identities
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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. The fundamental Pythagorean Identity states that sin²θ + cos²θ = .
2. Dividing sin²θ + cos²θ = 1 by cos²θ yields the identity = sec²θ.
3. Dividing sin²θ + cos²θ = 1 by sin²θ yields the identity 1 + cot²θ = .
4. Which of the following is equivalent to 1 - sin²θ?
cos²θ
sec²θ
tan²θ
csc²θ
5. If tan θ = 3, what is sec²θ?
3
4
9
10
6. Simplify the expression (sec²θ - 1) / tan²θ using Pythagorean Identities.
7. Prove the identity: tanθ + cotθ = secθ cscθ.
8. The expression (1 - cos²θ) is equal to tan²θ.
True
False
9. If csc²θ = 5, then cot²θ = 4.
True
False
10. Given that cosθ = 4/5 and θ is in Quadrant IV, find the exact values of sinθ, tanθ, cotθ, secθ, and cscθ using Pythagorean Identities.