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Flip to reveal answersState the Pythagorean identity.
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All 9 Flashcards — Pythagorean identity
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Question
State the Pythagorean identity.
Answer
sin²θ + cos²θ = 1, for every angle θ.
Question
Rearrange for sin²θ.
Answer
sin²θ = 1 − cos²θ.
Question
Rearrange for cos²θ.
Answer
cos²θ = 1 − sin²θ.
Question
How do you find sin θ from cos θ?
Answer
sin θ = ±√(1 − cos²θ); pick the sign from the quadrant.
Question
Given cos θ = 2/3 (acute), find sin θ.
Answer
sin²θ = 1 − 4/9 = 5/9 ⇒ sin θ = √5/3.
Question
Simplify 1 − sin²θ.
Answer
cos²θ.
Question
Simplify 1 − cos²θ.
Answer
sin²θ.
Question
Why must you watch the sign when rooting?
Answer
√ gives only the magnitude; the quadrant decides + or −.
Question
Key move when proving a trig identity?
Answer
Replace 1 − sin²θ or 1 − cos²θ with the other square, then cancel.
Read the notes
Full study notes for Pythagorean identity
Topic 3.6 hub
Identities & double angles
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Math AA SL exam skills
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