Question

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

Answer 1

`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`