SOLUTION: What is the general solution for {{{sin2x=-1/2}}}?

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Question 1104138: What is the general solution for sin2x=-1%2F2?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+sin%28+2x+%29+=+-1%2F2+
Let +2x+=+z+
+sin%28+z+%29+=+-1%2F2+
The sin function is negative in
the 3rd and 4th quadrants
----------------------------
+z+=+pi+%2B+pi%2F6+%2B+2n%2Api+
+z+=+2pi+-+pi%2F6+%2B+2n%2Api+
------------------------------
+2x+=+pi+%2B+pi%2F6+%2B+2n%2Api+
+x+=+pi%2F2+%2B+pi%2F12+%2B+n%2Api+
+x+=+%28+7pi+%29%2F12+%2B+n%2Api+
and
+2x+=+2pi+-+pi%2F6+%2B+2n%2Api+
+x+=+pi+-+pi%2F12+%2B+n%2Api+
+x+=+%28+11pi+%29%2F12+%2B+n%2Api+
-----------------------------
check:
suppose +n+=+3+
+x+=+%28+7pi+%29%2F12+%2B+3pi+
+2x+=+%287pi%29%2F6++%2B+6pi+
-------------------------
+6pi+ takes you back to +0pi+
and
+%287pi%29%2F6+=+pi+%2B+pi%2F6+
and
+sin%28+%287pi%29%2F6+%29+=+-1%2F2++
OK