How do you find the exact value of tan1(tan(2π3))?

1 Answer
Aug 6, 2015

These are inverses of each other. tan1(x) (or arctanx) is the inverse of tan(x).

Let A(x) be a function, and let A1(x) be its inverse (note that this is not the same as the reciprocal).

Then, the function composition of A1(x) with A(x) is A1(A(x))=x.

Since the domain of tanx is (π2,π2)±πk (where k is in the set of integers), and the period is π, take the coterminal angle to be π3.

So the exact answer is π3.