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Math Help - coordinates and trigonometry

  1. #1
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    coordinates and trigonometry

    I have to find the coordinates for S(i).

    My attempt :

    OP = 1 * 1/2 = 1/2

    (1/2)2 + x2 = 12

    x = √(3)/2

    cos-1(√(3)/2) = 30

    sin-1(1/2) = 30

    t = 30

    cos(2*t) = cos(60) = 1/2

    sin(2*t) = sin(60) =√(3)/2

    S(i) = (1,2 , √(3)/2 )
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: coordinates and trigonometry

    t is not 30. t is arctan(1/2). And so your coordinates (cos(2t),sin(2t)) = ?
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  3. #3
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    Re: coordinates and trigonometry

    Can you try to explain why t= arctan(1/2) because I can't see it.
    And can't I use arccos and arcsin instead of arctan?
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: coordinates and trigonometry

    The angle of inclination of a line having slope m is \tan^{-1}(m).

    m=\frac{\Delta y}{\Delta x}=\tan(\theta)\,\therefore\,\theta=\tan^{-1}(m).

    Now, use the double-angle identities for sine and cosine and:

    \sin(\tan^{-1}(x))=\frac{x}{\sqrt{x^2+1}}

    \cos(\tan^{-1}(x))=\frac{1}{\sqrt{x^2+1}}
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  5. #5
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    Re: coordinates and trigonometry

    Thank you.
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