math

Find the parametric equations of a circle centered at the origin with radius of 4 where you start at point (-4,0) at s=0 and you travel counterclockwise with a period of 2π.

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  1. x = a cos s
    y = a sin s

    when s = 0, x = -4
    so =-4 = a cos 0 = a
    so
    x = - 4 cos s
    when s = pi/2 , y = -4
    so -4 = a sin pi/2 = a
    so y = -4 sin s

  2. you know that
    y = 4 sint
    x = 4 cost
    starts at (4,0)
    You are 180° out of phase, starting at (-4,0)
    So,
    y = 4sin(t+π)
    x = 4cos(t+π)
    and Damon's equations work.

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