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Math Help - Solve the equation??

  1. #1
    Newbie Viky's Avatar
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    Red face Solve the equation??

    If -180o <= 180o , solve the equation

    cos(2theta - 70o) = sin(theta+40o)
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  2. #2
    MHF Contributor
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    Talking

    Quote Originally Posted by Viky View Post
    If -180o <= 180o , solve the equation

    cos(2theta - 70o) = sin(theta+40o)
    A good start would probably to apply sum and difference identities, so you can get \sin(\theta) and \cos(\theta) by themselves, and then work from there.

    . . . . . \cos(2\theta\, -\, 70^{\circ})\, =\, \cos(2\theta)\cos(70^{\circ})\, +\, \sin(2\theta)\sin(70^{\circ})

    . . . . . \sin(\theta\, +\, 40^{\circ})\, =\, \sin(\theta)\cos(40^{\circ})\, +\, \cos(\theta)\sin(40^{\circ})

    And note also the double-angle identities:

    . . . . . \cos(2\theta)\, =\, \cos^2(\theta)\, -\, \sin^2(\theta)

    . . . . . \sin(2\theta)\, =\, 2\sin(\theta)\cos(\theta)

    See where this leads....

    If you get stuck please reply showing your steps and how far you have gotten. Thank you!
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  3. #3
    Newbie Viky's Avatar
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    thanks

    how do i insert the theta symbol?
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  4. #4
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    mr fantastic's Avatar
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    Quote Originally Posted by Viky View Post
    how do i insert the theta symbol?
    Type [tex]\theta[/tex].

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