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!

Homework Help: 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

    Mark44

    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

    rock.freak667

    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

    Mentallic

    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

    Mark44

    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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook