document.write( "Question 1029573: Solve the equation for x if 0 ≤ x < 2π. Give your answer in radians using exact values only. (Enter your answers as a comma-separated list.)
\n" ); document.write( "2 sin2 x + cos x − 1 = 0
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Algebra.Com's Answer #644558 by stanbon(75887) $\"\"$ $\"About$

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Solve the equation for x if 0 ≤ x < 2π. Give your answer in radians using exact values only. (Enter your answers as a comma-separated list.)
\n" ); document.write( "2 sin^2(x) + cos x − 1 = 0
\n" ); document.write( "===========
\n" ); document.write( "2(1-cos^2(x)) + cos(x) -1 = 0
\n" ); document.write( "------------
\n" ); document.write( "-2cos^2(x) + cos(x) +1 = 0
\n" ); document.write( "-----------------------------------
\n" ); document.write( "cos^2(x) - cos(x) - 1 = 0
\n" ); document.write( "------------------------------
\n" ); document.write( "Use the quadratic formula to find potential values of cos(x)
\n" ); document.write( "cos(x) = [1 +- sqrt(1-4*-1)]/2 = [1+-sqrt(5)]/2
\n" ); document.write( "cos(x) = (1+sqrt(5))/2 :: extraneous
\n" ); document.write( "cos(x) = (1-sqrt(5))/2 = -0.6180
\n" ); document.write( "x = arccos(-0.6180) = 2.2370 radians or 4.0462 radians
\n" ); document.write( "---------------
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

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