1. find the exact value of cos2θ if sin 2θ=3/4 and θ is between 0° and 90°
1 answer:
Answer:
<u>Identities used:</u>
- sin²θ + cos²θ = 1
- cos2θ = cos²θ - sin²θ
#1
- sin2θ = 3/4, and θ in the first quadrant
- cos²2θ = 1 - sin²2θ
- cos2θ = √(1 - sin²2θ) = √(1 - 9/16) = √(7/16) = √7 / 4
#2
- sinθ(cos²θ - cos2θ) =
- sinθ(cos²θ - (cos²θ - sin²θ) =
- sinθ(sin²θ) =
- sin³θ
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