Question

arctan[tan(7pi /4)] how does the answer exist? I thought 7pi/4 wasn't in the domain?

Answer 1

the domain of arctan is all real numbers
what you mean is that \(\frac{7\pi}{4}\) is not in the RANGE so the obvious answer of \(\frac{7\pi}{4}\) is wrong

Answer 2

you have to find an angle (number) between \(-\frac{\pi}{2}\) and \(\frac{\pi}{2}\) that has the same tangent
that is how you get your answer

Answer 3

thank you so much

Answer 4

there is my lousy picture of \(\frac{7\pi}{4}\) and you can see that it is co terminal with \(-\frac{\pi}{4}\) and that therefore \(\tan(\frac{7\pi}{4})=\tan(-\frac{\pi}{4})\) so you pick that angle as your answer