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Math Help - sketch parameter curve

  1. #1
    Senior Member furor celtica's Avatar
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    sketch parameter curve

    sketch this curve given in terms of the parameter alpha
    x = cos alpha, y = sin alpha
    i got x= 0 for y = 1, -1 and y = 0 for x = 1,-1 but from here i dont know how to sketch the graph! any suggestions?
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  2. #2
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    Quote Originally Posted by furor celtica View Post
    sketch this curve given in terms of the parameter alpha
    x = cos alpha, y = sin alpha
    i got x= 0 for y = 1, -1 and y = 0 for x = 1,-1 but from here i dont know how to sketch the graph! any suggestions?
    Obviously you are using degrees as argument of the trigonometric functions. So choose those values of \alpha where you know the trig values:

    \alpha = 60^\circ \rightarrow x = \frac12, y = \pm \frac12 \sqrt{3}

    \alpha = 30^\circ \rightarrow x = \frac12 \sqrt{3}, y = \pm \frac12

    and so on ...
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  3. #3
    Senior Member furor celtica's Avatar
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    not really, this is less trigonometry than solving equations involving a parameter and Cartesian variables!
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  4. #4
    Super Member
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    Quote Originally Posted by furor celtica View Post
    not really, this is less trigonometry than solving equations involving a parameter and Cartesian variables!
    Given
    x = \cos(\alpha)
    y=\sin(\alpha)

    Square both sides of both equations and add columnwise:

    x^2+y^2=(\cos(\alpha))^2+(\sin(\alpha))^2 = 1

    which is the equation of the unit circle around the origin.
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