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Sine & Cosine Problems

  1. Nov 9, 2003 #1
    I'm unsure as to whether I'm correct with this:

    4sinx - 3cosx

    My answer ended up being 5sin(x + sin^-1 (-3/5)).

    The equations I used were:

    asinx + bcosx = (a^2 + b^2)^1/2 * sin(x + angle)
    angle = sin^-1 (b / (a^2 + b^2)^1/2))

    Can someone clarify whether I'm correct? I would appreciate it.
     
  2. jcsd
  3. Nov 9, 2003 #2

    Hurkyl

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    A good way to check your answer is to reverse the process using the angle addition identity:

    sin (θ + φ) = sin θ cos φ + cos θ sin φ

    And using the facts

    sin arcsin (3/5) = 3/5
    and
    cos arcsin (3/5) = 4/5. (why?)
     
  4. Nov 10, 2003 #3
    I checked my answer and it equals the original equation, but have I fully solved it?
     
  5. Nov 11, 2003 #4

    Hurkyl

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    If it checks (and I agree that it does), then yep!
     
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