document.write( "Question 325522: Find all solutions for the following equations.Record your answer in exact form where possible.
\n" ); document.write( "(a) \"2\"\"%22cos%22%5E2x\"\"%22%22=%22%22\"\"-3\"\"%22sin%22\"\"x\"
\n" ); document.write( "(b) \"%22sin%22\"\"x\"\"%22%22%2A%22%22\"\"%22tan%22\"\"x\"\"%22%22=%22%22\"\"%22sin%22\"\"x\"
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\n" ); document.write( " Thinking I may have to us Half-angle formula on these (not sure)
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Algebra.Com's Answer #233857 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Find all solutions for the following equations.Record your answer in exact form where possible.
\n" ); document.write( "(a) \"2\"\"%22cos%22%5E2x\"\"%22%22=%22%22\"\"-3\"\"%22sin%22\"\"x\"
\n" ); document.write( "(b) \"%22sin%22\"\"x\"\"%22%22%2A%22%22\"\"%22tan%22\"\"x\"\"%22%22=%22%22\"\"%22sin%22\"\"x\"
\n" ); document.write( "
\n" ); document.write( " Thinking I may have to us Half-angle formula on these (not sure)
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\r\n" );
document.write( "No you don't need those.\r\n" );
document.write( "\r\n" );
document.write( "\"2\"\"%22cos%22%5E2x\"\"%22%22=%22%22\"\"-3\"\"%22sin%22\"\"x\"\r\n" );
document.write( "\r\n" );
document.write( "Use the identity:  \"%22sin%22%5E2theta\"\"%22%22%2B%22%22\"\"%22cos%22%5E2theta\"\"%22%22=%22%22\"\"1\" written as \"%22cos%22%5E2theta\"\"%22%22=%22%22\"\"1\"\"%22%22-%22%22\"\"%22sin%22%5E2theta\" to rewrite the left side:\r\n" );
document.write( "\r\n" );
document.write( "\"2\"\"%281-%22sin%22%5E2x%29\"\"%22%22=%22%22\"\"-3\"\"%22sin%22\"\"x\"\r\n" );
document.write( "\r\n" );
document.write( "\"2\"\"%22%22-%22%22\"\"2\"\"%22sin%22%5E2x\"\"%22%22=%22%22\"\"-3\"\"%22sin%22\"\"x\"\r\n" );
document.write( "\r\n" );
document.write( "Get 0 on the right:\r\n" );
document.write( "\r\n" );
document.write( "\"2\"\"%22%22-%22%22\"\"2\"\"%22sin%22%5E2x\"\"%22%22%2B%22%22\"\"3\"\"%22sin%22\"\"x\"\"%22%22=%22%22\"\"0\"\r\n" );
document.write( "\r\n" );
document.write( "Rearrange terms on the left in descending order:\r\n" );
document.write( "\r\n" );
document.write( "\"-2\"\"%22sin%22%5E2x\"\"%22%22%2B%22%22\"\"3\"\"%22sin%22\"\"x\"\"%22%22%2B%22%22\"\"2\"\"%22%22=%22%22\"\"0\"\r\n" );
document.write( "\r\n" );
document.write( "To make factoring easier, multiply through by -1\r\n" );
document.write( "\r\n" );
document.write( "\"2\"\"%22sin%22%5E2x\"\"%22%22-%22%22\"\"3\"\"%22sin%22\"\"x\"\"%22%22-%22%22\"\"2\"\"%22%22=%22%22\"\"0\"\r\n" );
document.write( "\r\n" );
document.write( "\"%22%28sin%22\"\"x\"\"%22%22-%22%22\"\"%222%29%28%22\"\"2\"\"%22sin%22\"\"x\"\"%22%22%2B%22%22\"\"%221%29%22\"\"%22%22=%22%22\"\"0\"\r\n" );
document.write( "\r\n" );
document.write( "Setting the first factor = 0\r\n" );
document.write( "\r\n" );
document.write( "\"%22sin%22\"\"x\"\"%22%22-%22%22\"\"2\"\"%22%22=%22%22\"\"0\"\r\n" );
document.write( "\r\n" );
document.write( "\"%22sin%22\"\"x\"\"%22%22=%22%22\"\"2\"\r\n" );
document.write( "\r\n" );
document.write( "This is impossible because no sine can be greater than 1 or\r\n" );
document.write( "less than -1.\r\n" );
document.write( "\r\n" );
document.write( "Setting the second factor = 0\r\n" );
document.write( "\r\n" );
document.write( "\"2\"\"%22sin%22\"\"x\"\"%22%22%2B%22%22\"\"%221%22\"\"%22%22=%22%22\"\"0\"\r\n" );
document.write( "\r\n" );
document.write( "\"2\"\"%22sin%22\"\"x\"\"%22%22=%22%22\"\"%22-1%22\"\r\n" );
document.write( "\r\n" );
document.write( "\"%22sin%22\"\"x\"\"%22%22=%22%22\"\"-1%2F2\"\r\n" );
document.write( "\r\n" );
document.write( "All angles in QIII and QIV  with reference angle 30° (or \"pi%2F6\"\r\n" );
document.write( "if your teacher wants radians) are solutions.\r\n" );
document.write( "\r\n" );
document.write( "In degrees:\r\n" );
document.write( "\"x\"\"%22%22=%22%22\"\"%22210%B0%2Bn%2A360%B0%22\"; \"x\"\"%22%22=%22%22\"\"%22330%B0%2Bn%2A360%B0%22\"\r\n" );
document.write( "\r\n" );
document.write( "In radians:\r\n" );
document.write( "\"x\"\"%22%22=%22%22\"\"7pi%2F6%2B2pi%2An\";\"x\"\"%22%22=%22%22\"\"11pi%2F6%2B2pi%2An\"\r\n" );
document.write( " \r\n" );
document.write( "--------------------------------\r\n" );
document.write( "--------------------------------\r\n" );
document.write( "--------------------------------\r\n" );
document.write( "\r\n" );
document.write( "\"%22sin%22\"\"x\"\"%22%22%2A%22%22\"\"%22tan%22\"\"x\"\"%22%22=%22%22\"\"%22sin%22\"\"x\"\r\n" );
document.write( "\r\n" );
document.write( "Get 0 on the right:\r\n" );
document.write( "\r\n" );
document.write( "\"%22sin%22\"\"x\"\"%22%22%2A%22%22\"\"%22tan%22\"\"x\"\"%22%22-%22%22\"\"%22sin%22\"\"x\"\"%22%22=%22%22\"\"0\"\r\n" );
document.write( "\r\n" );
document.write( "Factor out \"%22sin%22\"\"x\" on the left side:\r\n" );
document.write( "\r\n" );
document.write( "\"%22sin%22\"\"x\"\"%22%28tan%22\"\"x\"\"%22%22-%22%22\"\"%221%29%22\"\"%22%22=%22%22\"\"0\"\r\n" );
document.write( "\r\n" );
document.write( "Setting the first factor = 0\r\n" );
document.write( "\r\n" );
document.write( "\"%22sin%22\"\"x\"\"%22%22=%22%22\"\"0\"\r\n" );
document.write( "\r\n" );
document.write( "All angles with reference angle 0 are solutions:\r\n" );
document.write( "\r\n" );
document.write( "In degrees:\r\n" );
document.write( "\"x\"\"%22%22=%22%22\"\"%22n%2A180%B0%22\"\r\n" );
document.write( "\r\n" );
document.write( "In radians:\r\n" );
document.write( "\"x\"\"%22%22=%22%22\"\"n%2Api\";\r\n" );
document.write( "\r\n" );
document.write( "Setting the second factor = 0\r\n" );
document.write( "\r\n" );
document.write( "\"%22tan%22\"\"x\"\"%22%22-%22%22\"\"%221%22\"\"%22%22=%22%22\"\"0\"\r\n" );
document.write( "\r\n" );
document.write( "\"%22tan%22\"\"x\"\"%22%22=%22%22\"\"%221%22\"\r\n" );
document.write( "\r\n" );
document.write( "All angles in QI and QIII  with reference angle 45° (or \"pi%2F4\"\r\n" );
document.write( "if your teacher wants radians) are solutions.\r\n" );
document.write( "\r\n" );
document.write( "In degrees:\r\n" );
document.write( "\"x\"\"%22%22=%22%22\"\"%2245%B0%2Bn%2A360%B0%22\"; \"x\"\"%22%22=%22%22\"\"%22225%B0%2Bn%2A360%B0%22\"\r\n" );
document.write( "\r\n" );
document.write( "In radians:\r\n" );
document.write( "\"x\"\"%22%22=%22%22\"\"pi%2F4%2B2pi%2An\";\"x\"\"%22%22=%22%22\"\"7pi%2F4%2B2pi%2An\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
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