SOLUTION: Find the exact value for cos2x given sinx = √2/2?

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Question 935570: Find the exact value for cos2x given sinx = √2/2?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Divide top and bottom by +sqrt%28+2+%29+
+sqrt%282%29+%2F+2+=+1+%2F+sqrt%28+2+%29+
---------------------------
+sin%28+x+%29+=+a%2Fc+
label the components:
+a%2Fc+=+1%2Fsqrt%282%29+
Find the horizontal component
+b%5E2+=+c%5E2+-+a%5E2+
+b%5E2+=+%28sqrt%282%29%29%5E2+-+1%5E2+
+b%5E2+=+2+-+1+
+b%5E2+=+1+
+b+=+1+
+b+=+-1+
---------------
+cos%28x%29+=+b%2Fc+
+cos%28+x+%29+=+1%2Fsqrt%282%29+
+x+=+pi%2F4+
and, also
+cos%28+x+%29+=+-1%2Fsqrt%282%29+
+x+=+3pi%2F4+
-----------------------
+2x+=+pi%2F2+
and
+2x+=+3pi%2F2+
-----------------
Finally,
+cos%28+2x+%29+=+0+
In both of these cases