Inequalities (trig) + Attempted

[lovemake1]

Homework Statement

tanx + 3cotx = 4

Homework Equations

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.

please help,
thanks.

 

[rock.freak667]

The same way you solved tanx=1

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

 

[lovemake1]

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

 

[rock.freak667]

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

Unfortunately there is not.

 

[lovemake1]

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

 

[eumyang]

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.

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

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

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

 

[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?

 

[rock.freak667]

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?

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

 

[lovemake1]

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

 

[rock.freak667]

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

Yes they are correct.