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Math Help - Trigonometric Formulars

  1. #1
    Junior Member
    Joined
    Feb 2006
    Posts
    29

    Trigonometric Formulars

    Have I got this right or have I failed miserably as usual

    Given that <br />
0<\theta<\frac{1}{2}pi<br />

    and <br />
sin (\theta)= \frac{1}{4}<br />

    using appropriate trigonometric formulas find the exact values of the following
    <br />
(i)   cos(2\theta)<br />
    Use
    <br />
cos(2\theta) = 1-2 sin^2\theta<br />
    gives
    <br />
cos(2\theta) = 1-2 * \frac{1}{4}^2 = \frac{7}{8}<br />

    <br />
(ii)   cos(\theta)<br />
    use
    <br />
cos(\theta) = \pm \sqrt{1-sin^2\theta}<br />
    gives
    <br />
cos(\theta) = \pm \sqrt{1-\frac{1}{4}^2}= \pm\sqrt{\frac{15}{16}} = \frac{1}{4}\sqrt{15}<br />

    Positive in this case

    <br />
(iii)   sin(3\theta)<br />

    Rewrite as
    <br />
sin(2\theta+\theta)<br />

    find <br />
sin(2\theta)<br />
using <br />
sin(2\theta) = 2 sin\theta cos \theta<br />

    <br />
sin(2\theta) = 2 * \frac {1}{4}*\frac{1}{4}\sqrt{15} = \frac{1}{8}\sqrt{15}<br />


    and then use

    <br />
sin(\phi+\theta) = sin\phi cos\theta + cos\phi sin\theta<br />

    Giving

    <br />
sin(2\theta+\theta) = \frac{1}{8}\sqrt{15}*\frac{1}{4}\sqrt{15} + \frac{7}{8}*\frac{1}{4} = \frac{11}{16}<br />

    So

    <br />
sin(3\theta) =  \frac{11}{16}<br />

    Again positive
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  2. #2
    Member
    Joined
    Nov 2005
    From
    Wethersfield, CT
    Posts
    92
    Greetings:

    Your work is well organized and, in the case at hand, 100% correct! Nice work. Now we need only work on that confidence. You are not a "failed miserably as usual" kind of person. You are learning a complex discipline and, from what I can see, you are learning well!

    Regards,

    Rich B.
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  3. #3
    Junior Member
    Joined
    Feb 2006
    Posts
    29
    Quote Originally Posted by Rich B.
    Greetings:

    Your work is well organized and, in the case at hand, 100% correct! Nice work. Now we need only work on that confidence. You are not a "failed miserably as usual" kind of person. You are learning a complex discipline and, from what I can see, you are learning well!

    Regards,

    Rich B.
    Thanks that's given me a big confidence boost !!
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