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How do I solve for theta?

  1. Mar 5, 2010 #1
    1. The problem statement, all variables and given/known data

    This is originally from a physics problem but it's more of a math question. How do I solve for theta?

    2. Relevant equations

    400 - Tcos(theta) = 0

    -200 + Tsin(theta) = 0

    Using those equations, I need to solve for theta. Also, knowing that tan(theta) = sin(theta)/cos(theta) is supposed to be relevant to this.

    3. The attempt at a solution

    All I did was simplify the equations to 200 - Tcos(theta) + Tsin(theta) = 0

    Not sure if that was a good idea or not but I'm suck.
  2. jcsd
  3. Mar 5, 2010 #2


    Staff: Mentor

    Your equations can be rewritten as
    Tsin(theta) = 200
    Tcos(theta) = 400

    Instead of adding equations to each other, what about dividing each side of one equation by the corresponding side of the other?
  4. Mar 5, 2010 #3


    User Avatar
    Homework Helper

    Place all the constants on one side of the equality for each of the equations.

    Then remember that sin2θ+cosθ=1.

    so something like R2sin2θ+R2cos2θ=1
  5. Mar 5, 2010 #4
    Do you mean as in like this?

    tan(theta) = 200/400

    Is this legal?
  6. Mar 5, 2010 #5


    User Avatar
    Homework Helper

    Yes :smile:

    You can even take a slower approach to solve the two simultaneous equations:

    [tex]Tsin\theta=200[/tex] (1)

    [tex]Tcos\theta=400[/tex] (2)

    Re-arrange (1) : [tex]T=200csc\theta[/tex] (3)

    Substitute (3) into (2) : [tex]200csc\theta cos\theta=400[/tex]

    Simplify : [tex]tan\theta=1/2[/tex]

    So yes, if you are convinced that substitution is a valid step in solving simultaneously, then the process of dividing both equations together is also.
  7. Mar 6, 2010 #6


    Staff: Mentor

    Sure, it's legal, as long as T isn't 0, and I'm reasonably sure in this problem it isn't. Once you get a value for theta, then substitute into either of the original equations to find T.
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