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!

Trig problem I can't see into

  1. Aug 16, 2008 #1
    1. The problem statement, all variables and given/known data

    [tex]\sqrt{}3[/tex]sinx-3cosx=0 solve in interval [0,2[tex]\pi[/tex])

    2. Relevant equations

    reciprocal identities, pythagorean identities, confunction identities, Even/odd identities, sum/difference formulas, double angle formulas, power reducing formulas, half-angle formulas, sum to product formulas, product to sum formulas. I am not sure how many of those are relevant but thats all the identities and formulas I have learned so far.

    3. The attempt at a solution

    To be quite honest I don't even know where to start with this problem : ( mostly the square root of three is throwing me. I have been trying to solve this for days so if anyone could so much as tell me what formulas or identites to use i would appreciate it. I'm just so lost.

    Oh also I'm new to this forum, just found it tonight, so i just want to say hi to everyone!
     
  2. jcsd
  3. Aug 16, 2008 #2

    rock.freak667

    User Avatar
    Homework Helper

    [tex]\sqrt{3}sinx-3cosx=0 \Rightarrow \sqrt{3}sinx=3cosx[/tex]

    Can you divide by cosx and go from there?
     
  4. Aug 16, 2008 #3

    Gib Z

    User Avatar
    Homework Helper

    Welcome to PF Geekchick =]

    In general, for things like a sin x +/- b cos x, we can combine them into a single sine term, using something known as the Auxiliary Angle method: http://en.wikipedia.org/wiki/Trigonometric_identity#Linear_combinations

    EDIT: Damn, too late and a longer method. lol
     
  5. Aug 16, 2008 #4
    Thank you! Thank you! thank you! I didn't even think about the fact that sin/cos is equal to tan duh! *smacks head* I was trying to make things way more complicated. So just to be sure once I divide by cos I'm left with the (square root of 3)tan=3 which after dividing that by the (square root of 3) and simplifying I have tan= square root of 3 which in the interval [0,2pi) means my answer is (pi/3) and (4pi/3). Yay!
     
  6. Aug 19, 2008 #5

    dynamicsolo

    User Avatar
    Homework Helper

    The "auxiliary angle" method is fine -- it's just "overkill" on the equation

    a sin x + b cos x = c

    in the case where c = 0. When you follow through with it for this problem, you get

    [tex]sin(x - \frac{4 \pi}{3}) = 0 \Rightarrow x - \frac{4 \pi}{3} = ..., -\pi, 0, \pi, ...[/tex]

    with the results in the fundamental circle being the two Geekchick has found. (I'm just elaborating on this since it's always good to know multiple methods for solving a problem and to confirm that they all give the same answer.)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Similar Discussions: Trig problem I can't see into
Loading...