How do you find sin (x/2), given cos x = -5/8, with π/2 < x < π?

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Answer 1 · 2016-10-29T17:49:01

$sin(x/2) = sqrt(13)/4$ Please see the explanation.

Use the identity from this source Half Angle Identities :

$sin^2(x/2) = 1/2(1 - cos(x))$

$sin^2(x/2) = 1/2(1 + 5/8)$

$sin^2(x/2) = 13/16$

$sin(x/2) = +-sqrt(13)/4$

Because we are told that $pi/2 < x < pi$ , we know that the sine function is positive, therefore, we drop the negative:

$sin(x/2) = sqrt(13)/4$