Practice Pythagorean Identity (2.2) - Theorems in Geometry & Trigonometry

Practise this section

9 questions

Flashcard drill
3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
Using the Pythagorean identity, find cos(θ) if sin(θ) = 0.8.
Show hintHide hint
Use the formula cos²(θ) = 1 - sin²(θ).
Question 2.
If sin(45°) is √2/2, what is cos(45°) using the Pythagorean identity?
Show hintHide hint
Remember that sin and cos are equal at 45 degrees.
3Question 3.
What is the Pythagorean identity?
- sin²θ + cos²θ = 2
- sin²θ + cos²θ = 1
- sin²θ + cos²θ = 0
Show hintHide hint
Remember that all sine and cosine functions combine to equal 1.
4Question 4.
If sin(θ) = 0.3, what is cos²(θ)?
- True
- False
Show hintHide hint
Think about how cosine and sine relate to each other.
Question 5.
Given sin(θ) = 0.5 find all angles θ possible in degrees using the Pythagorean identity.
Show hintHide hint
Consider the sine curve and where it reaches 0.5.
Question 6.
If you know sin(30°) = 0.5, show step-by-step how to find cos(30°) and verify the identity.
Show hintHide hint
Work through the calculations to prove it's correct.

5 more questions in this section. Enroll free to practise them all.