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Suppose cosx=-2/7 and π/2<x<π.

+2 votes

Find sin x/2.?

asked Feb 22, 2013 in TRIGONOMETRY by Jose Rodriguez Rookie

1 Answer

+2 votes

cos(x) = -2/7

Half-Angle formulas: sin(θ/2) = ± √[(1-cosθ)/2]

sin(x/2) = ± √[(1-cos(x))/2]

But cos(x) = -2/7.

sin(x/2) = ± √[(1 - (-2/7))/2]

sin(x/2) = ± √[(1 + (2/7))/2]

Rewrite the expression with common denominator.

sin(x/2) = ± √[((7 + 2)/7)/2]

sin(x/2) = ± √[(9/7)/2]

sin(x/2) = ± √[9/14]

sin(x/2) = ± √9/√14

sin(x/2) = ± 3/√14.

answered Feb 22, 2013 by richardson Scholar

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