Adding Multiples of 2π to arctan(stuff) Answers: Is This Correct?

[GreenPrint]

I feel kind of dumb asking this (it's been a while sense I took precalc) but I always thought that if I had something like

arctan(stuff) = answer
that if I added any whole integer multiple of 2pi to the answer I would get equivalent answers. Is this correct? Like
answer - 4pi = answer -2pi = answer + 2pi = answer + 4 pi

you get different angles but they can still act as correct answers to
arctan(stuff)?

 

[SammyS]

I feel kind of dumb asking this (it's been a while sense I took precalc) but I always thought that if I had something like

arctan(stuff) = answer
that if I added any whole integer multiple of 2pi to the answer I would get equivalent answers. Is this correct? Like
answer - 4pi = answer -2pi = answer + 2pi = answer + 4 pi

you get different angles but they can still act as correct answers to
arctan(stuff)?

tan(x) is periodic with a period of π .

So if you have arctan(stuff) = answer , then adding any integer multiple of π to 'answer,' will give 'another answer'.

In other words, if tan('answer') = stuff, then it's also true that tan('another answer') = stuff .

 

[GreenPrint]

ok well in this case i can add multiples of two pi's as well than?

 

[SammyS]

ok well in this case i can add multiples of two pi's as well than?

Sure, since 2π is an integer multiple of π .