document.write( "Question 524726: Find the EXACT solutions of the equation sin(x)+2cos^2(x)=1 that are in the interval [0, 2π). \n" ); document.write( "

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Find the EXACT solutions of the equation sin(x)+2cos^2(x)=1 that are in the interval [0, 2π)
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\n" ); document.write( "sin(x)+2cos^2(x)=1
\n" ); document.write( "sin(x)+2(1-sin^2(x)=1
\n" ); document.write( "sin(x)+2-2sin^2(x)=1
\n" ); document.write( "2sin^2(x)-sin(x)-1=0
\n" ); document.write( "(2sin(x)+1)(sin(x)-1)=0
\n" ); document.write( "(2sin(x)+1)=0
\n" ); document.write( "2sin(x)=-1
\n" ); document.write( "sin(x)=-1/2
\n" ); document.write( "x=7π/6 and 11π/6 (in quadrants III and IV where sin<0)
\n" ); document.write( "or
\n" ); document.write( "sin(x)-1=0
\n" ); document.write( "sin(x)=1
\n" ); document.write( "x=π/2
\n" ); document.write( "ans:
\n" ); document.write( "Solutions: 7π/6, 11π/6, and π/2 \n" ); document.write( "

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