If costheta =2sqrt5/5 and 0degrees< 0<90degrees what is sintheta/2?

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Answer 1 · 2018-04-23T01:04:33

#sin (theta/2) = sqrt{1/10 (5 - 2 sqrt{5})) #

Let's remember the double angle formula for cosine:

#cos (2x) = 2 cos^2 x - 1 = 1- 2 sin^2 x#

The latter form is what we need here.

#sin x = pm sqrt{ 1/2 (1 - cos(2x)) }#

Here we have #theta = x/2# so

#sin (theta/2) = pm sqrt{1/2 (1 -{ 2 sqrt{5}} /5) } #

Since #theta>0# in the first quadrant, #theta/2# is in the first quadrant as well so the sign of the sine is positive.

#sin (theta/2) = sqrt{1/10 (5 - 2 sqrt{5})) #

Let's leave it there.