document.write( "Question 985594: Find all solutions of the equation in the interval [0,2π).\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"+4cos%5E2%28x%29=5+-+4+sin%28x%29+\"\r
\n" ); document.write( "\n" ); document.write( "Write your answer in radians in terms of π.
\n" ); document.write( "If there is more than one solution, separate them with commas.
\n" ); document.write( "

Algebra.Com's Answer #606440 by Alan3354(69443)\"\" \"About 
You can put this solution on YOUR website!
Find all solutions of the equation in the interval [0,2π).\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"+4cos%5E2%28x%29=5+-+4+sin%28x%29+\"
\n" ); document.write( "--------------
\n" ); document.write( "Sub 1 - sin^2 for cos^2, then it's a quadratic.
\n" ); document.write( "---
\n" ); document.write( "4 - 4sin^2 = 5 - 4sin
\n" ); document.write( "4sin^2 - 4sin + 1 = 0
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"4x%5E2%2B-4x%2B1+=+0\") has the following solutons:
\n" ); document.write( "
\n" ); document.write( " \"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
\n" ); document.write( "
\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
\n" ); document.write( "
\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%28-4%29%5E2-4%2A4%2A1=0\".
\n" ); document.write( "
\n" ); document.write( " Discriminant d=0 is zero! That means that there is only one solution: \"x+=+%28-%28-4%29%29%2F2%5C4\".
\n" ); document.write( " Expression can be factored: \"4x%5E2%2B-4x%2B1+=+%28x-0.5%29%2A%28x-0.5%29\"
\n" ); document.write( "
\n" ); document.write( " Again, the answer is: 0.5, 0.5.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-4%2Ax%2B1+%29\"

\n" ); document.write( "\n" ); document.write( "========================
\n" ); document.write( "sin(x) = 1/2
\n" ); document.write( "x = pi/6, 5pi/6
\n" ); document.write( "
\n" );