If cos(θ) = -15/17, and θ is in Quadrant II, then what is sin(θ/2)? Give an exact answer, using radicals as needed. Simplify your answer completely. sin(θ/2) =
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We can use the Pythagorean identity sin^2(θ) + cos^2(θ) = 1 to find sin(θ). sin^2(θ) = 1 - cos^2(θ) = 1 - (-15/17)^2 = 1 - 225/289 = 64/289 So, sin(θ) = ±√(64/289). Since θ is in Quadrant II, sin(θ) is positive. Therefore, sin(θ) = √(64/289) = 8/17. Show more…
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