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Solving trig equations using Addition formula

  1. Dec 4, 2011 #1
    1. The problem statement, all variables and given/known data

    Solve the equation: sin(x+∏/6)=2cosx for 0≤x≤2∏

    2. Relevant equations

    sinAcosB+cosAsinB

    3. The attempt at a solution

    sin(x+∏/6)=2cosx

    2cosx=(√3)/2sinx+1/2cosx

    How do I solve from here?
     
  2. jcsd
  3. Dec 4, 2011 #2

    micromass

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    Moved the thread to precalc. Please post in the correct forum next time.
     
  4. Dec 4, 2011 #3

    I like Serena

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    Hi studentxlol! :smile:

    Perhaps you can use the following trig identity?

    a sin x + b cos x = √(a2+b2) sin(x+ϕ)

    where cos ϕ = a/√(a2+b2)
    and sin ϕ= b/√(a2+b2)
     
  5. Dec 5, 2011 #4

    HallsofIvy

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    The first, obvious, step is to subtract (1/2) cos(x) from both sides. Then get a tangent.
     
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