document.write( "Question 816116: solve tanx cosx= 1/2 for all values of x. \n" ); document.write( "

Algebra.Com's Answer #491398 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"tan%28x%29cos%28x%29+=+1%2F2\"$
\n" ); document.write( "One way to solve this is to start by replacing tan with sin/cos:
\n" ); document.write( " $\"%28sin%28x%29%2Fcos%28x%29%29cos%28x%29+=+1%2F2\"$
\n" ); document.write( "The cos's cancel:
\n" ); document.write( " $\"sin%28x%29+=+1%2F2\"$
\n" ); document.write( "We should recognize that 1/2 is a special angle value for sin. It tells us that the reference angle is $\"pi%2F6\"$ . Since the 1/2 is positive and sin is positive in the 1st and 2nd quadrants, we should get the following general solution equations:
\n" ); document.write( " $\"x+=+pi%2F6+%2B+2pi%2An\"$ (for the 1st quadrant)
\n" ); document.write( " $\"x+=+pi-pi%2F6+%2B+2pi%2An\"$ (for the 2nd quadrant)
\n" ); document.write( "The second equation will simplify:
\n" ); document.write( " $\"x+=+5pi%2F6+%2B+2pi%2An\"$

\n" ); document.write( "The problem asks for all values of x. This is what the general solution is. So all the solutions are described by:
\n" ); document.write( " $\"x+=+pi%2F6+%2B+2pi%2An\"$
\n" ); document.write( " $\"x+=+5pi%2F6+%2B+2pi%2An\"$ \n" ); document.write( "

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