Suppose cosx=-2/7 and π/2<x<π.

Question

Find sin x/2.?

Answer 1

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.