nicolemadison03 nicolemadison03

25-10-2020
Mathematics

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given cos x= 1/4 with 0 < x < pi/2 find cos x/2

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LammettHash LammettHash

25-10-2020

Since 0 < x < π/2, we know 0 < x/2 < π/4, so that cos(x/2) is still positive.

Recall the double-angle formula,

cos²(x/2) = (1 + cos(x)) / 2

so that

cos(x/2) = √((1 + 1/4) / 2) = √(5/8)

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