SOLUTION: solve tanx cosx= 1/2 for all values of x.

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Question 816116: solve tanx cosx= 1/2 for all values of x.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
tan%28x%29cos%28x%29+=+1%2F2
One way to solve this is to start by replacing tan with sin/cos:
%28sin%28x%29%2Fcos%28x%29%29cos%28x%29+=+1%2F2
The cos's cancel:
sin%28x%29+=+1%2F2
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:
x+=+pi%2F6+%2B+2pi%2An (for the 1st quadrant)
x+=+pi-pi%2F6+%2B+2pi%2An (for the 2nd quadrant)
The second equation will simplify:
x+=+5pi%2F6+%2B+2pi%2An

The problem asks for all values of x. This is what the general solution is. So all the solutions are described by:
x+=+pi%2F6+%2B+2pi%2An
x+=+5pi%2F6+%2B+2pi%2An