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Find cos θ, given that sin θ = -√2/2, and pi <= θ <= 38*pi/2?
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The reference angler is pi/4, but since doin is negative we know it must be 5pi/4 or 7pi/4. Keep adding multiples of pi to those until you exceed 38pi/2 and you have your solution set.
cosθ=sqrt(1-sin^2θ)=sqrt2/2