document.write( "Question 1156517: Please help me to answer this! Thank you :\r
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document.write( "5 + 2cos x - 8sin^2 x = 0 \n" );
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Algebra.Com's Answer #779237 by Theo(13342)![]() ![]() You can put this solution on YOUR website! start with 5 + 2 * cos(x) - 8 * sin^2(x) = 0 \n" ); document.write( "since sin^2(x) + cos^2(x) = 1, then sdin^2(x) = 1 - cos^2(x). \n" ); document.write( "replace sin^2(x) with that to get: \n" ); document.write( "5 + 2 * cos(x) - 8 * (1 - cos^2(x)) = 0 \n" ); document.write( "simplify to get: \n" ); document.write( "5 + 2 * cos(x) - 8 + 8 * cos^2(x) = 0 \n" ); document.write( "order the equation in descending order of degree and combine like terms to get: \n" ); document.write( "8 * cos^2(x) + 2 * cos(x) - 3 = 0 \n" ); document.write( "factor this quadratic equation to get: \n" ); document.write( "cos(x) = -.75 or .5 \n" ); document.write( "assume these are both positive and solve for x in the first quadrant to get: \n" ); document.write( "x = 41.40962211 degrees or x = 60 degrees. \n" ); document.write( "cosine = -.75 is negative which means the angle has to be in the second and third quadrant. \n" ); document.write( "x = 180 - 41.40962211 in the second quadrant = 138.5903779 degrees. \n" ); document.write( "x = 180 + 41.40962211 in the third quadrant = 221.4096221 degrees. \n" ); document.write( "cosine = .5 is positive which means the angle has to be in the first and fourth quadrant. \n" ); document.write( "x = 60 degrees in the first quadrant. \n" ); document.write( "x = 360 - 60 = 300 degrees in the fourth quadrant. \n" ); document.write( "your angle can be 60, 138.5903779, 221.4096221, and 300 degrees. \n" ); document.write( "this is confirmed by the graph of the equation shown below.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " ![]() \n" ); document.write( " \n" ); document.write( " |