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Two Simultaneous Eqns with Trig, Statcs Problem

  1. Sep 8, 2014 #1
    1. The problem statement, all variables and given/known data

    I'm doing a statics problem and am following how the solutions manual does it but they skipped a few steps and I'm lost as a result.

    I have two equations and two unknowns: F and θ (degrees)

    2. Relevant equations

    Equation 1: F*cos(25+θ) = -54.684
    Equation 2: F*sin(25+θ) = 69.131

    3. The attempt at a solution

    Solve for F: F=-54.684/cos(25+θ)

    Plug F into other equation and combine sin and cos to get tangent(25+θ):

    -54.684*tan(25+θ)=69.131
    tan(25+θ)=(-1.26)
    25+θ=arctan(-1.26)
    25+θ=-51.65
    θ=-76.65

    The solutions manual simply says "Solving Equations (1) and (2) yields 25+θ=128.35; θ=103 degrees; F = 88.1 lb"

    The only thing I can think of is adding 180 degrees to the θ I got which gives me the 103 degrees they got. Any ideas?
     
  2. jcsd
  3. Sep 8, 2014 #2

    Mark44

    Staff: Mentor

    Sounds good to me. The tangent function is periodic with period π (or 180°), so adding 180° to what you got will produce an angle in the second quadrant. Presumably any angle you get should be between 0° and 180°.

    BTW, you could have shortened your work by dividing the 2nd equation by the first. That would have eliminated F in one step and gotten you directly to tan(25 + θ) on one side of the equation.
     
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