document.write( "Question 451699: I would appreciate some help with these two questions:\r
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Algebra.Com's Answer #310605 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
I would appreciate some help with these two questions:
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document.write( "Solve each question for 0 ≦ Ꮎ < 2p\r\n" );
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document.write( "1. \"2cos%5E2%28theta%29-1=0\"\r\n" );
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document.write( "\"2cos%5E2%28theta%29=1\"\r\n" );
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document.write( "\"cos%5E2%28theta%29=1%2F2\"\r\n" );
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document.write( "Use the principle of square roots:\r\n" );
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document.write( "\"cos%28theta%29=+%22%22+%2B-+sqrt%281%2F2%29\"\r\n" );
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document.write( "\"cos%28theta%29=%22%22+%2B-+sqrt%28expr%281%2F2%29expr%282%2F2%29%29\"\r\n" );
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document.write( "\"cos%28theta%29=%22%22+%2B-+sqrt%282%2F4%29\"\r\n" );
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document.write( "\"cos%28theta%29=%22%22+%2B-+sqrt%282%29%2F2%29\"\r\n" );
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document.write( "Since the cosine can be positive or negative,\r\n" );
document.write( "The solutions are all the angles in all four \r\n" );
document.write( "quadrants with a 45² or \"pi%2F4\" reference \r\n" );
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document.write( "They are:\r\n" );
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document.write( "\"pi%2F4\", \"3pi%2F4\", \"5pi%2F4\", \"7pi%2F4\"   \r\n" );
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document.write( "2. \"sqrt%282%29sin%28theta%29cos%28theta%29%2Bcos%28theta%29=0\"\r\n" );
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document.write( "Factor out GCF \"cos%28theta%29\"\r\n" );
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document.write( "\"cos%28theta%29%28sqrt%282%29sin%28theta%29%2B1%29=0\"\r\n" );
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document.write( "Use the zero-factor property.  Setting the first\r\n" );
document.write( "factor = 0,\r\n" );
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document.write( "\"cos%28theta%29=0\"\r\n" );
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document.write( "This has solutions \"pi%2F2\", \"3pi%2F2\"\r\n" );
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document.write( "Setting the other factor = 0,\r\n" );
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document.write( "\"sqrt%282%29sin%28theta%29%2B1=0\"\r\n" );
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document.write( "\"sqrt%282%29sin%28theta%29=-1\"\r\n" );
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document.write( "\"sin%28theta%29=-1%2Fsqrt%282%29\"\r\n" );
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document.write( "\"sin%28theta%29=expr%28-1%2Fsqrt%282%29%29expr%28sqrt%282%29%2Fsqrt%282%29%29\"\r\n" );
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document.write( "\"sin%28theta%29=-sqrt%282%29%2F2%29\"\r\n" );
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document.write( "Since the sine is negative, the solutions are the \r\n" );
document.write( "angles in the third and fourth quadrants with a \r\n" );
document.write( "45² or \"pi%2F4\" reference angle.\r\n" );
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document.write( "They are \"5pi%2F4\" and \"7pi%2F4\"  \r\n" );
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document.write( "So the solutions are: \r\n" );
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document.write( "\"pi%2F2\", \"3pi%2F2\", \"5pi%2F4\", and \"7pi%2F4\"\r\n" );
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document.write( "Edwin
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