How do you find the exact value for $tan^-1(tan (7pi/4))$ ?

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Answer 1 · 2016-02-15T18:42:57

$kpi+3pi/4, k in ZZ$

$tan^-1(tan(7pi/4))$

By the trigonometric circle you can see that $tan(7pi/4)=tan(-pi/4)=-1$

So the expression simplifies in:

$tan^-1(-1)$

So which are the angles which tangent is -1?

Again by the trigonometric circle you can see that:

$tan^-1(-1)=kpi+3pi/4, k in ZZ$

How do you find the exact value for tan^-1(tan (7pi/4))tan^-1(tan (7pi/4))?