Homework Help: Inequalities (trig) + Attempted

1. Sep 27, 2010

lovemake1

1. The problem statement, all variables and given/known data

tanx + 3cotx = 4

2. Relevant equations

3. The attempt at a solution

Heres my attempt:

tanx + 3/tanx - 4 = 0
(tan^2x -4tanx + 3) / tanx = 0

tan^2x - 4 tanx + 3

(tanx - 3 ) (tanx - 1 ) = 0

tan = 3, tan = 1

im not sure about tan = 3, but for tan = 1 , pi/4 +180n,
is this correct? if it is how would i go about findin solutions for tan=3.

thanks.

2. Sep 27, 2010

rock.freak667

The same way you solved tanx=1

tanx=3, the principle angle is tan-1(3)

3. Sep 27, 2010

lovemake1

how would we represent tan^-1(3) interms of radians ?
calculators are not allowed in our school, is there a way ?

4. Sep 27, 2010

rock.freak667

Unfortunately there is not.

5. Sep 28, 2010

lovemake1

hmm..
so we just find solutions for tan = 1 ?

6. Sep 28, 2010

eumyang

"pi/4 +180n" -> Don't mix degree and radian measure. Also, state what "n" is. You should write
$$\frac{\pi}{4} + n \pi, n \in \mathbb{Z}$$

No, you still need both solutions. The other could be written as
$$\tan^{-1} 3 + n \pi, n \in \mathbb{Z}$$

7. Oct 2, 2010

lovemake1

tan^-1(3) + npi
how do you write that interms of pi?

i've never seen anything like that. could you please give me an example?

8. Oct 2, 2010

rock.freak667

you can't write tan-1(3) in terms of pi. That is why you have to leave it as is.

9. Oct 2, 2010

lovemake1

ok, just to make sure.. are my previous steps correct?
just to double check. thanks

10. Oct 2, 2010

rock.freak667

Yes they are correct.