1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Arctan equation

  1. Oct 9, 2012 #1
    1. The problem statement, all variables and given/known data

    Solve the following equation:

    [tex]arctan(x)+arctan(\sqrt{3}x)=\frac{7\pi}{12}[/tex]



    3. The attempt at a solution

    I multiplied by tan on both sides but since we can exactly calculate tan(7pi/12) i wasn't able to get an answer. Is there something else i can do? Thank you before hand.
     
  2. jcsd
  3. Oct 9, 2012 #2

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    That's not multiplying by the tangent, that's taking the tangent of both sides.

    After that, do you know the angle addition identity for tangent?

    [itex]\displaystyle \tan(\alpha + \beta) = \frac{\tan \alpha + \tan \beta}{1- \tan \alpha \tan \beta}[/itex]
     
  4. Oct 9, 2012 #3
    yes that's exactly what i did and I got:

    [tex]1+\sqrt{3}x=tan(\frac{7\pi}{12})-\sqrt{3}x^{2}tan(\frac{7\pi}{12})[/tex]

    Should i factor out with tan on the right side to get tan(7pi/12)(1-√3x^2) or what?


    I know the answer will be x=1 because arctan(1)+arctan(sqrt(3))=pi/4+pi/3=7pi/12
     
    Last edited: Oct 9, 2012
  5. Oct 9, 2012 #4

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    I get [itex](1+\sqrt{3})x=tan(\frac{7\pi}{12})-\sqrt{3}x^{2}tan(\frac{7\pi}{12})\ .[/itex]

    I would divide by tan(7π/12).

    Write in standard form for a quadratic equation.

    Have you evaluated tan(7π/12) ?
     
  6. Oct 9, 2012 #5
    nevermind i got it because tan(7pi/12) is tan(pi/4+pi/3)
     
  7. Oct 9, 2012 #6

    CAF123

    User Avatar
    Gold Member

    Using the relation provided by SammyS, hopefully you got to [tex]\arctan\frac{x + \sqrt{3}x}{1-\sqrt{3}x^2} = \frac{7\pi}{12} [/tex]

    Take tangent of both sides: [itex] \tan(\frac{7\pi}{12}) [/itex] as a sum of two angles and use the double angle relation (again) to find this.

    Equate the above two and solve for x
     
  8. Oct 9, 2012 #7

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Beware of possible extraneous solutions.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook