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General solution

  1. Jun 15, 2009 #1
    1. The problem statement, all variables and given/known data

    h(x)=cos(x+30) and g(x) = -2sinx

    Determine the general solution without the use of a calculator, if
    h(x)=g(x)

    2. Relevant equations

    trig identities, trig ratios, double angle formulae, reduction formulae.

    3. The attempt at a solution

    cos(x+30)=-2sinx
    sin(90-x-30)=-2sinx
    sin(60-x)=-2sinx


    can't get rid of the 2 in front of sinx. Need help:confused:
     
  2. jcsd
  3. Jun 15, 2009 #2
    Use the Angle sum and difference identities.

    In this case:

    [tex]\cos(\alpha \pm \beta) = \cos \alpha \cos \beta \mp \sin \alpha \sin \beta\,[/tex]

    Just substitute for alpha=x and beta=30, and you'll come up with the solution of cos(x+30).

    Regards.
     
  4. Jun 15, 2009 #3
    Thank you very much Дьявол
     
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