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Math Help - Trigonometric

  1. #1
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    Trigonometric

    Given that sin20=x, cos10=y, state each of the following in terms of x and y
    a) cos30
    b) cos 5
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  2. #2
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    Re: Trigonometric

    Quote Originally Posted by Trefoil2727 View Post
    Given that sin20=x, cos10=y, state each of the following in terms of x and y
    a) cos30
    b) cos 5
    a) \cos(30^o)=\cos(10^o+20^o)

    b) \cos(5^o)=\cos\left(\frac{10^o}{2}\right).

    Now you show some work on your part.
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  3. #3
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    Re: Trigonometric

    This is part a:

    There is the identity \cos(\theta + \phi) = \cos{\theta}\cos{\phi} - \sin{\theta}\sin{\phi}

    let \space \sin{\theta} = \sin{20^{\circ}} = x \space and \space \cos{\phi} = \cos{10^{\circ}} = y

    that makes \space \cos{20^{\circ} = \sqrt{1 - x^2} \space and \space \sin{10^{\circ} = \sqrt{1 - y^2}

    where \space \theta = 20^{\circ} \space \phi = 10^{\circ}
    Last edited by jpritch422; June 12th 2013 at 06:28 PM.
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