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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