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Thread: need some help with trig function: 4 sin(a + pi/6) cos(a - pi/6)

  1. #1
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    need some help with trig function: 4 sin(a + pi/6) cos(a - pi/6)

    So i basically hate to solve this thing:

    . . . . .[tex]4\, \sin\left(\alpha\, +\, \dfrac{\pi}{6}\right)\, \cos\left(\alpha\, -\, \dfrac{\pi}{6}\right)[/tex]
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  2. #2
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    You would do well to find the Double Angle formula for sine. Hint: [tex]\sin(2x) = ...[/tex]
    "Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.

  3. #3
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    tkhunny's suggestion is particularly apt if the expression is

    4 sin(alpha + pi/6) cos(alpha + pi/6)

    But it looks to me more like

    4 sin(alpha + pi/6) cos(alpha - pi/6)

    Am I right about that? (I'm also not sure I'm reading the "alpha" correctly.)

    If so, then there are some identities called "product-to-sum" identities you can use; if you haven't seen them, they can be derived from the angle-sum and angle-difference identities.

    Does any of that sound familiar?

  4. #4
    Elite Member stapel's Avatar
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    Cool

    Quote Originally Posted by chaNio View Post
    So i basically hate to solve this thing:

    . . . . .[tex]4\, \sin\left(\alpha\, +\, \dfrac{\pi}{6}\right)\, \cos\left(\alpha\, -\, \dfrac{\pi}{6}\right)[/tex]
    There is no "equals", so this is not an "equation" and cannot be "solved". What were the actual instructions?

    When you reply, please include a clear listing of your thoughts and efforts so far. Thank you!

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