Question 1142024: if sinx=-3/4 and x is the third quadrant find cos(x/2)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! first find arcsin(3/4)
it will be equal to 48.59037789 degrees.
the equivalent angle in the third quadrant is 180 + that = 228.5903779 degrees.
to confirm, find the sine of that.
it will be equal to -.75 which is the same as -3/4.
cos(that angle / 2) = cos(114.29511889) = -.4114378278.
that should be your answer.
if you used the half angle formula, you would get:
cos(x/2) = plus or minus sqrt ( (1 + cos(x) / 2 )
(1 + cos(x)) / 2 = 1 + cos(228.5903779) / 2 = (1 - .6614378278) / 2 = .1692810861.
plus or minus sqrt (.1692810861) = .4114378278.
since cosine is negative in second or third quadrant, then cos(x/2) = -.4114378278.
the solution was determined in two ways.
first was by dividing the angle in the third quadrant by two and find the cosine of that.
second was using the half angle formula.
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