SOLUTION: Find sin (x + y) if sin x = ¾ and cos y = 2/3 with both angles in the first quadrant.

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Question 950351: Find sin (x + y) if sin x = ¾ and cos y = 2/3 with both angles in the first quadrant.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Use the identity:
+sin%28+x%2By+%29+=+sin%28x%29%2Acos%28y%29+%2B+cos%28x%29%2Asin%28y%29+
+sin%28x%29+=+3%2F4+
+cos%28y%29+=+2%2F3+
------------------------
Also, use the identities:
+cos%28x%29+=+sqrt%28+1+-+sin%28x%29%5E2+%29+
+sin%28y%29+=+sqrt%28+1+-+cos%28y%29%5E2+%29+
---------------------------------------
+cos%28x%29+=+sqrt%28+1+-+%283%2F4%29%5E2+%29+
+sin%28y%29+=+sqrt%28+1+-+%282%2F3%29%5E2+%29+
---------------------------------------
+cos%28x%29+=+sqrt%28+1+-+9%2F16+%29+
+sin%28y%29+=+sqrt%28+1+-+4%2F9+%29+
--------------------------------------
+cos%28x%29+=+sqrt%28+7%2F16+%29+
+sin%28y%29+=+sqrt%28+5%2F9+%29+
---------------------------------
+cos%28x%29+=+sqrt%287%29%2F4+
+sin%28y%29+=+sqrt%285%29%2F3+
------------------------------
+sin%28+x%2By+%29+=+sin%28x%29%2Acos%28y%29+%2B+cos%28x%29%2Asin%28y%29+

+sin%28+x%2By+%29+=+1%2F2+%2B+sqrt%2835%29%2F12+
Hope I got it