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Math Help - Compound angle formulae

  1. #1
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    Compound angle formulae

    1.cos 19pi/12

    2.If sin A =3/5 with 0<A<pi/2 and cos B=1/3 with 0<B<pi/2 calculate...
    a)cos(A+B) b)sin(A+B) c)cos2B d)sin2A

    Can someone help me with 1., 2a) and d)... I'll try b) and c) and post it up later to see if it's right.

    Thank you!
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  2. #2
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    Drawing a little diagram might help you.

    sinA = 3/5 means that cosA = 4/5
    cosB = 1/3 means that sinB = \frac{\sqrt{8}}{3}

    using cos(A+B) = cosAcosB - sinAsinB, I got  cos(A+B) = \frac{4-3\sqrt{8}}{15}

    It's a similar story with the others. Just use those values of sinA, sinB, cosA, cosB and keep substituting in the relevant double angle formulae.
    Last edited by WWTL@WHL; January 13th 2008 at 02:44 PM.
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  3. #3
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    Quote Originally Posted by johett View Post
    1.cos 19pi/12
    [snip]
    cos 19pi/12 = cos 5pi/12. Note that 5pi/12 = pi/6 + pi/4. Apply cos(A+B) = cosAcosB - sinAsinB.
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