SOLUTION: Find all theta in the interval [0,2pi) that satisfy the equation. sin 2theta = 1/ sqrt 2

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Question 894379: Find all theta in the interval [0,2pi) that satisfy the equation.
sin 2theta = 1/ sqrt 2
Found 2 solutions by Fombitz, josmiceli:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Do you mean sin%5E2%28theta%29 or sin%282%2Atheta%29??

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I'll say +alpha+=+2%2Atheta+
+sin+%28+alpha+%29+=+1%2Fsqrt%282%29+
+alpha+=+pi%2F4+
also
+alpha+=+%283%2Api%29%2F4+
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sin functions in the 3rd and 4th quadrants are
negative, so I can't include these
------------------------------
Now I can say:
+2%2Atheta+=+alpha+
+theta+=+alpha%2F2+
+theta+=+%28+pi%2F4+%29+%2F+2+
+theta+=+pi%2F8+
and
+theta+=+%28%28+3%2Api+%29%2F4+%29+%2F+2+
+theta++=+%28+3%2Api+%29%2F8+