# 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.