Solve the equation tan(12(x−π4))=−1 for x∈[−2π,2π]. How do I solve for x?

1 Answer
Apr 21, 2018

#x=195/48pi and 199/48pi#

Explanation:

First, set the interior of the tan(x) function equal to a constant, say "u". You now have the equation:

#tan(u)=-1#

Solving for u using the inverse tangent function, you get

#u=(3pi)/4# and #u=(7pi)/4#

You can now just solve for x by replacing u with the original contents.

#u=12(x-4pi)#

Therefore

#12(x-4pi)=(3pi)/4#

and

#12(x-4pi)=(7pi)/4#

You can simplify these equations to find x. I will just show the work for the first solution.

#x-4pi=(3pi)/48#

#x=(3pi)/48+4pi#

#x=195/48pi#

The other solution is

#x=199/48pi#

Thus, #x=195/48pi and 199/48pi#