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

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Answer 1 · 2018-04-21T04:15:19

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

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, $x=195/48pi and 199/48pi$