1. Limited time only! Sign up for a free 30min personal 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!

Solving a trigonometry equation simultaneously in two variables

  1. Aug 5, 2014 #1
    1. The problem statement, all variables and given/known data

    Solve the equations sin(x+2y)=1/2 , cos(2x-y)=1/ sqrt(2)


    2. Relevant equations



    3. The attempt at a solution
    I tried getting a generic solution for both the first and second equation. How do I further proceed? By simultaneously solving? I so, how?

    2x-y=2m*pi + or - pi/4

    x+2y=n*pi + (-1)^n * pi/6
     
  2. jcsd
  3. Aug 5, 2014 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Yes, solve those two equations simultaneously. For example, if you were to multiply the first equation by 2, getting [itex]4x- 2y= 3m\pi\pm \pi/2[/itex]. Now, adding that to the second equation eliminates "y" from the equation.
     
  4. Aug 5, 2014 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You seem to be saying you do not know how to solve the two equations
    [tex] 2x - y = a\\x + 2y = b [/tex]
    for ##x, y## in terms of ##a,b##. Is that really true, or have you just not 'recognized' the problem correctly?
     
  5. Aug 7, 2014 #4
    I'm in 11th grade, doing IIT pre-prep as extra classes.
    I do know how to solve simultaneous equations :P. However, I was wondering whether the +- part would affect solving simultaneous equations, because I want a general solution for x and y e.g. n*pi + pi/4 or something.
     
  6. Aug 7, 2014 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Well, yes, it will 'affect' the answer but the way the answer is affected is just basic algebra. Have you done as I suggested?
     
  7. Aug 7, 2014 #6
    i am not sure but i think we can solve it
    as
    (x+2y)=sin(inverse)1/2=30(degree)
    2x-y=cos(inverse)1/sqrt2=90(degree)
    amusing 1 and 2 equation
    multiply 2 equation by 2
    then we will get x=24(degree)
    and y=3(degree)
     
  8. Aug 7, 2014 #7

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Welcome to PF;
    Well spotted.
    The thing is that sin(a)=1/2, not just for for a=30°, but also for a=150° and many other angles besides. In degrees, the full equation goes like:

    ##a = 180n + 30\times (-1)^n: n=0,1,2,3,\cdots##

    This is what is in post #1, with a=x+2y (right at the bottom) - except that PhysicsKid703 is using radians instead of degrees.
     
  9. Aug 7, 2014 #8
    Hmm.
    Ok HallsofIvy, I understood what you said and I got the answer written in the back of the book. Thanks so much for the help.
    SimonsBridge- Yes, thats the general equation for all the values of theta when sin theta = sin alpha. Thats in fact exactly how it appears as a formula in my text.
     
  10. Aug 7, 2014 #9

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Did you understand where that relation came from?
    I was thinking that you could use the same sort of observation to get rid of the ##\pm## for the cosine part. Just look at the series of values of "a" that make cos(a)=1/√2 true and try to express them using the (-1)^n style of notation. (hint: 2n-1 is always an odd number for n=1,2,3...).

    But you managed to get the "correct" answer anyway so... well done :)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Solving a trigonometry equation simultaneously in two variables
Loading...