document.write( "Question 1042505: Solve sin^2θ − 5cosθ = 5 for 0°≤θ≤360° \n" ); document.write( "
Algebra.Com's Answer #657503 by ikleyn(52879)\"\" \"About 
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\n" ); document.write( "Solve sin^2(theta) - 5cos(theta) = 5 for 0° <= theta < 360°.
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document.write( "Replace \"sin%5E2%28theta%29\" by \"1+-+cos%5E2%28theta%29\" to have the equation for \"cos%28theta%29\" only. You will get\r\n" );
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document.write( "\"1-cos%5E2%28theta%29+-+5cos%28theta%29\" = \"5\",  or\r\n" );
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document.write( "\"cos%5E2%28theta%29+%2B+5cos%28theta%29+%2B+4\" = \"0\".\r\n" );
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document.write( "Factor left side:\r\n" );
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document.write( "\"%28cos%28theta%29%2B4%29%2A%28cos%28theta%29+%2B1%29\" = \"0\".\r\n" );
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document.write( "Then the equation deploys in two equations:\r\n" );
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document.write( "1)  \"cos%28theta%29+%2B+4\" = \"0\",  or  \"cos%28theta%29\" = \"-4\",  which has no solutions,  and\r\n" );
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document.write( "2)  \"cos%28theta%29+%2B+1\" = \"0\",  or  \"cos%28theta%29\" = \"-1\",  which has the solution \"theta\" = 180°.\r\n" );
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document.write( "Answer.  The solution is \"theta\" = 180°.\r\n" );
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