Question #aa440

1 Answer
Douglas K.
Nov 21, 2016

cos(x/2) = sqrt(5)/5

Explanation:

The phrase; "and it is obtuse", must mean that halving the angle moves from the 2nd quadrant to the 1st quadrant, because cos(x) = -3/5 is either 2nd or 3rd quadrant.

Use the identity:

cos(x/2) = +-sqrt((1 + cos(x))/2)

but drop the - because we are in the 1st quadrant:

cos(x/2) = sqrt((1 - 3/5)/2)

cos(x/2) = sqrt((1 - 3/5)/2(5/5))

cos(x/2) = sqrt((5 - 3)/10)

cos(x/2) = sqrt(2/10)

cos(x/2) = sqrt(1/5)

cos(x/2) = sqrt(5)/5

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