document.write( "Question 866318: How many points in the interval 0 ≤ x ≤ 2π satisfy the equation cos 2x = –2 sin x?
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #522228 by stanbon(75887) $\"\"$ $\"About$

You can put this solution on YOUR website!
How many points in the interval 0 ≤ x ≤ 2π satisfy the equation cos 2x = –2 sin x?
\n" ); document.write( "---------------------
\n" ); document.write( "cos(2x) = -2sin(x)
\n" ); document.write( "------
\n" ); document.write( "1-2sin^2(x) = -2sin(x)
\n" ); document.write( "----
\n" ); document.write( "2sin^2(x) -2sin(x) - 1 = 0
\n" ); document.write( "------
\n" ); document.write( "sin((x) = [2 +- sqrt(4-4*2*-1)]/4
\n" ); document.write( "------
\n" ); document.write( "sin(x) = [2+-sqrt(12)]/4
\n" ); document.write( "------
\n" ); document.write( "sin(x = [2[1+-sqrt(3)]/4
\n" ); document.write( "------
\n" ); document.write( "sin(x) = (1/2)(1+sqrt(3)) or sin(x) = (1/2)(1-sqrt(3))
\n" ); document.write( "----
\n" ); document.write( "Note:: (1/2)(1+sqrt(3) > 1 so no solutions there
\n" ); document.write( "-----
\n" ); document.write( "(1/2)(1-sqrt(3)) = -0.3660, so there are 2 solutions,
\n" ); document.write( "one in QIII, the other in QIV.
\n" ); document.write( "--------------------------------
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
\n" ); document.write( "------------------- \n" ); document.write( "

\n" );