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Need help solving this trig equation

  1. Mar 26, 2017 #1
    1. The problem statement, all variables and given/known data
    what's the best way to solve this equation: 3cos(θ) + 1.595*sin(θ) = 3.114

    2. Relevant equations
    (sinθ)^2 + (cosθ)^2 = 1

    3. The attempt at a solution
    I tried using the identity above to solve this equation and ended up with cosθ = +/- 1.0526.
     
  2. jcsd
  3. Mar 26, 2017 #2
    Could you show your steps for your solution?
     
  4. Mar 26, 2017 #3
    so since (sinθ)^2 + (cosθ)^2 = 1, I solved for sinθ and got sqrt(1 - (cosθ)^2). Then I subtituted it in to the equation 3cos(θ) + 1.595*sin(θ) = 3.114 and solved for θ.
     
  5. Mar 26, 2017 #4

    vela

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    Well, that's obviously wrong because -1 ≤ cos θ ≤ 1, and 1.0526 is outside that range. Your approach should work though.

    Another approach is to use
    $$a \cos\theta + b \sin\theta = \sqrt{a^2+b^2} \cos(\theta-\phi)$$ where ##\tan\phi = b/a##.
     
  6. Mar 26, 2017 #5
    could you pls show me how you got that equation?
     
  7. Mar 26, 2017 #6

    vela

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    Consider a right triangle below and use the identity ##\cos(\theta-\phi) = \cos\theta\,\cos\phi + \sin\theta\,\sin\phi##.

    triangle.png
     
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