math (trig)
posted by aziiancaligirl .
Find sin(x/2) if sin(x)= 0.4 and 3pi/2 < or equal to (x) < or equal to 2pi
Let's use cos 2A = 1  2sin^{2} A
and we can match
cos x = 1  2sin^{2} (x/2)
so we will need cos x
we know sin x = .4 and x is in the fourth quadrant, so the cosine will be positive.
Drawing a right angled triangle with side 2 and hypotenuse 5 ( .4 = 4/10 = 2/5), and using Pythagoras it is easy to see that cos x = √21/5
then:
√21/5 = 1  2sin^{2} (x/2)
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I got sin (x/2) = √(5√21)/√10 or appr.2043
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