document.write( "Question 1178312: Find all solutions in the interval [0,2pi)\r
\n" ); document.write( "\n" ); document.write( "2cos^2x-3=3sinx \n" ); document.write( "

Algebra.Com's Answer #807531 by MathLover1(20849) $\"\"$ $\"About$

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\n" ); document.write( " $\"2cos%5E2%28x%29-3=3sin%28x%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2cos%5E2%28x%29=3sin%28x%29%2B3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"cos%282+x%29+%2B+1=3sin%28x%29%2B3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"cos%282+x%29+=3sin%28x%29%2B3-1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"cos%5E2%28x%29+-+sin%5E2%28x%29+=3sin%28x%29%2B2\"$ ............ $\"cos%5E2%28x%29=1-sin%5E2%28x%29+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"1-sin%5E2%28x%29++-+sin%5E2%28x%29+=3sin%28x%29%2B2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"1-2sin%5E2%28x%29+=3sin%28x%29%2B2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2sin%5E2%28x%29%2B3sin%28x%29%2B2-1=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2sin%5E2%28x%29%2B3sin%28x%29%2B1=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2sin%5E2%28x%29%2B2sin%28x%29%2Bsin%28x%29%2B1=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%282sin%5E2%28x%29%2Bsin%28x%29%29%2B%282sin%28x%29%2B1%29=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"sin%28x%29%282sin%28x%29%2B1%29%2B%282sin%28x%29%2B1%29=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28sin%28x%29%2B1%29%282sin%28x%29%2B1%29=0\"$ \r
\n" ); document.write( "\n" ); document.write( "solutions:\r
\n" ); document.write( "\n" ); document.write( "if $\"%28sin%28x%29%2B1%29=0\"$ => $\"sin%28x%29=-1\"$
\n" ); document.write( "then\r
\n" ); document.write( "\n" ); document.write( " $\"x=sin%5E-1%28-1%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=+-pi%2F2\"$ ....periodicity of sin is $\"2pi\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=+2pi-pi%2F2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=+3pi%2F2%2B2pi%2An\"$ \r
\n" ); document.write( "\n" ); document.write( "in interval [ $\"0\"$ , $\"2pi\"$ )\r
\n" ); document.write( "\n" ); document.write( " $\"x=+270\"$ °\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "if $\"2sin%28x%29%2B1=0\"$ -> $\"sin%28x%29=-1%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=sin%5E-1%28-1%2F2%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=-pi%2F6\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=2pi-pi%2F6\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=11pi%2F6%2B2pi%2An\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=+7pi%2F6%2B2pi%2An\"$ \r
\n" ); document.write( "\n" ); document.write( "in interval [ $\"0\"$ , $\"2pi\"$ )\r
\n" ); document.write( "\n" ); document.write( " $\"+x=+210\"$ ° \r
\n" ); document.write( "\n" ); document.write( " $\"x=+330\"$ ° \r
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