Inequalities (trig) + Attempted

  • Thread starter lovemake1
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  • #1
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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.
 

Answers and Replies

  • #2
rock.freak667
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The same way you solved tanx=1

tanx=3, the principle angle is tan-1(3)
 
  • #3
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how would we represent tan^-1(3) interms of radians ?
calculators are not allowed in our school, is there a way ?
 
  • #4
rock.freak667
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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.
 
  • #5
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hmm..
so we just find solutions for tan = 1 ?
 
  • #6
eumyang
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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
[tex]\frac{\pi}{4} + n \pi, n \in \mathbb{Z}[/tex]

hmm..
so we just find solutions for tan = 1 ?
No, you still need both solutions. The other could be written as
[tex]\tan^{-1} 3 + n \pi, n \in \mathbb{Z}[/tex]
 
  • #7
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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
rock.freak667
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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.
 
  • #9
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ok, just to make sure.. are my previous steps correct?
just to double check. thanks
 
  • #10
rock.freak667
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ok, just to make sure.. are my previous steps correct?
just to double check. thanks
Yes they are correct.
 

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