cos/sin use 2npi and tan uses npi, but how do you know when to add 2npi or npi to the solution of the equation?

Answer 1

as you said, sin and cos have period of 2pi
and tan has period pi.

That's how you know.

Answer 2

I have an equation that is 3tan2x=3 and the solution is x=pi/12 + npi/3

and another equation that is 2tanx-2=0 , the answer sheet says the solution is x=5pi/4.

why is the npi not added to the second solution but it is on the first?

Answer 3

tan(kx) has period pi/k, since x grows k times faster.

So, I think you have a typo. It should be

3tan3x = 3
tan3x=1
now, you know that tan pi/4 = 1, so
3x = pi/4, and x = pi/12. Now, tan(3x) has period pi/3.

2tanx-2 = 0
tanx = 1
Since tan pi/4 = 1, tan (pi/4 + pi) = tan 5pi/4 =1 as well.

The 2nd has solutions at pi/4 + n*pi for any n. If they chose 5pi/4, there must have bee some conditions on the domain.

Answer 4

okay,
thanks!

Answer 5

ive had a problem where it goes cos pi/8 + npi and cos 2npi - 7pi/8. then you plug in for n to get the solutions. I'm not understanding where to put 2npi or npi it's not a period interval cause sin and cos are usually 2npi. Very confused when to put it or not put it.