Trig identities: problem involving tan and double angle forumlas

There is this problem:

If , express in terms of *a*.

I expressed tan in terms of and isolated it. I obtained .

But what about the sign? For example, for the first period should be positive for values of x greater than 0 and negative for values of x less than 0, but there does not seem to be anything in the expression I obtained that can account for the sign. Could somebody tell me what I have done wrong?

Thanks a lot.

Re: Trig identities: problem involving tan and double angle forumlas

Quote:

Originally Posted by

**Kurama** There is this problem:

If

, express

in terms of

*a*.

I expressed tan in terms of

and isolated it. I obtained

.

But what about the sign? For example, for the first period

should be positive for values of x greater than 0 and negative for values of x less than 0, but there does not seem to be anything in the expression I obtained that can account for the sign. Could somebody tell me what I have done wrong?

Thanks a lot.

the tangent function is positive in quad I , negative in quad II , positive in quad III and negative in quad IV ...

for ,

for ,

... and so on for quads III and IV