document.write( "Question 1104138: What is the general solution for $\"sin2x=-1%2F2\"$ ? \n" ); document.write( "

Algebra.Com's Answer #718873 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+sin%28+2x+%29+=+-1%2F2+\"$
\n" ); document.write( "Let $\"+2x+=+z+\"$
\n" ); document.write( " $\"+sin%28+z+%29+=+-1%2F2+\"$
\n" ); document.write( "The sin function is negative in
\n" ); document.write( "the 3rd and 4th quadrants
\n" ); document.write( "----------------------------
\n" ); document.write( " $\"+z+=+pi+%2B+pi%2F6+%2B+2n%2Api+\"$
\n" ); document.write( " $\"+z+=+2pi+-+pi%2F6+%2B+2n%2Api+\"$
\n" ); document.write( "------------------------------
\n" ); document.write( " $\"+2x+=+pi+%2B+pi%2F6+%2B+2n%2Api+\"$
\n" ); document.write( " $\"+x+=+pi%2F2+%2B+pi%2F12+%2B+n%2Api+\"$
\n" ); document.write( " $\"+x+=+%28+7pi+%29%2F12+%2B+n%2Api+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+2x+=+2pi+-+pi%2F6+%2B+2n%2Api+\"$
\n" ); document.write( " $\"+x+=+pi+-+pi%2F12+%2B+n%2Api+\"$
\n" ); document.write( " $\"+x+=+%28+11pi+%29%2F12+%2B+n%2Api+\"$
\n" ); document.write( "-----------------------------
\n" ); document.write( "check:
\n" ); document.write( "suppose $\"+n+=+3+\"$
\n" ); document.write( " $\"+x+=+%28+7pi+%29%2F12+%2B+3pi+\"$
\n" ); document.write( " $\"+2x+=+%287pi%29%2F6++%2B+6pi+\"$
\n" ); document.write( "-------------------------
\n" ); document.write( " $\"+6pi+\"$ takes you back to $\"+0pi+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+%287pi%29%2F6+=+pi+%2B+pi%2F6+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+sin%28+%287pi%29%2F6+%29+=+-1%2F2++\"$
\n" ); document.write( "OK\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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