Pythagorean Identities Worksheet

Pythagorean Identities Practice

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)?

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

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

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

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