SOLUTION: Find the exact value of {{{cos((1/2)cos^(-1)((-3)/4))}}}
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Question 138823: Find the exact value of
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
let
 )
so
=\cos\left(\frac{1}{2}\cos^{-1}\left(-\frac{3}{4}\right)\right))
=\cos\left(2*\frac{1}{2}\cos^{-1}\left(-\frac{3}{4}\right)\right))
Substitute "2u" in for "u"
=\cos\left(\cos^{-1}\left(-\frac{3}{4}\right)\right))
Multiply
=-\frac{3}{4})
Take the arccosine of the cosine of to get
-1=-\frac{3}{4})
Replace )
with -1)
=\frac{1}{4})
Add 1 to both sides
=\frac{1}{8})
Divide both sides by 2
=\sqrt{\frac{1}{8}})
Take the square root of both sides
=\frac{1}{\sqrt{8}})
Simplify
=\frac{\sqrt{2}}{4})
Rationalize the denominator if necessary
So \right)=\frac{\sqrt{2}}{4})
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