How do you use the unit circle to prove the double angle identity for sine and cosine functions?
Answer 1
Brittany Hodges
To prove the double angle identities using the unit circle, consider an angle θ on the unit circle. The coordinates of the point where the terminal side of θ intersects the unit circle are (cos(θ), sin(θ)). Using angle addition formulas, we derive sin(2θ) = 2sin(θ)cos(θ) and cos(2θ) = cos²(θ) – sin²(θ).
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