Pythagorean Identities Worksheet
Explore and apply the fundamental Pythagorean identities in trigonometry for Grade 9 students.
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Topics
Pythagorean Identities
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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 most fundamental Pythagorean identity is sin²θ + cos²θ = .
2. Dividing sin²θ + cos²θ = 1 by cos²θ gives the identity .
3. Dividing sin²θ + cos²θ = 1 by sin²θ gives the identity .
4. Which of the following is equivalent to 1 + cot²θ?
sec²θ
csc²θ
tan²θ
sin²θ
5. If sin θ = 3/5, use a Pythagorean identity to find the value of cos θ. Assume θ is in the first quadrant.
6. The identity 1 + tan²θ = sec²θ is derived by dividing sin²θ + cos²θ = 1 by sin²θ.
True
False
7. Simplify the expression (sec²x - 1) / tan²x using Pythagorean identities.