document.write( "Question 582240: solve for x using trigonometry for the interval [0, 2π)
\n" ); document.write( "sin^2x= 1/2
\n" ); document.write( "The x after the 2 is NOT a part of the exponent. \n" ); document.write( "

Algebra.Com's Answer #372243 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"%28sin%28x%29%29%5E2=1%2F2\"$
\n" ); document.write( "There is a positive and a negative value for $\"sin%28x%29\"$ .
\n" ); document.write( "The positive solution is:

\n" ); document.write( "The negative solution is: $\"sin%28x%29=-sqrt%281%2F2%29=-sqrt%282%29%2F2=sin%285pi%2F4%29=sin%287pi%2F4%29\"$
\n" ); document.write( "Those four angles $\"pi%2F4\"$ , $\"3pi%2F4\"$ , $\"5pi%2F4\"$ and $\"7pi%2F4\"$ are the solution.
\n" ); document.write( "The reference angle is $\"pi%2F4\"$ , or $\"45%5Eo\"$ for those allergic to $\"pi\"$ .
\n" ); document.write( "For each (first quadrant) reference angle there is, in each of the other quadrants, a \"reflection\" angle that has the same absolute value for all trigonometric functions. It is $\"pi-angle\"$ , the reflection on the y axis, for the second quadrant. It is $\"pi%2Bangle\"$ , the reflection on the origin, for the third quadrant, and $\"-angle\"$ , or $\"2pi-angle\"$ if you want it positive, the reflection on the x axis, for the third quadrant. \n" ); document.write( "

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