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Flip to reveal answersDouble-angle formula for sine?
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All 9 Flashcards — Double angles
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Question
Double-angle formula for sine?
Answer
sin 2θ = 2 sin θ cos θ (not 2 sin θ!).
Question
Three forms of cos 2θ?
Answer
cos²θ − sin²θ = 1 − 2sin²θ = 2cos²θ − 1.
Question
Which cos 2θ form if you only know sin θ?
Answer
1 − 2sin²θ.
Question
Which cos 2θ form if you only know cos θ?
Answer
2cos²θ − 1.
Question
Given sin θ = 3/5, cos θ = 4/5, find sin 2θ.
Answer
2(3/5)(4/5) = 24/25.
Question
Given cos θ = 4/5 (acute), find cos 2θ.
Answer
2(16/25) − 1 = 7/25.
Question
Simplify cos⁴θ − sin⁴θ.
Answer
(cos²−sin²)(cos²+sin²) = cos 2θ.
Question
Common double-angle mistake?
Answer
Writing sin 2θ = 2 sin θ (dropping cos θ).
Question
How do you start a double-angle exact-value problem?
Answer
Find sin θ and cos θ first (often via the Pythagorean identity), then substitute.
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Full study notes for Double angles
Topic 3.6 hub
Identities & double angles
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