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Math Help - intersection point

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    intersection point

    Find the intersection point of r cos(Ų - pi/4) = (2)^½ and r cosŲ = 1
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    Quote Originally Posted by cazimi View Post
    Find the intersection point of r cos(Ų - pi/4) = (2)^½ and r cosŲ = 1
    Must be a couple of people in the same class!

    Call phi = t for convenience.

    The first equation states:
    rcos(t - pi/4) = rcos(t)cos(pi/4) + rsin(t)sin(pi/4) = sqrt(2)

    or after some simplifying:
    rcos(t) + rsin(t) = 2

    Using the second equation gives:
    1 + rsin(t) = 2

    rsin(t) = 1

    Now, consider the two equations:
    rsin(t) = 1
    rcos(t) = 1

    Dividing the two gives:
    tan(t) = 1

    t = pi/4 + n*pi (where n = 0, 1, 2, 3, ...)

    Now
    r = 1/cos(t)

    So
    r = 1/cos(pi/4 + n*pi) = 1/[cos(pi/4)cos(n*pi) - sin(pi/4)*sin(n*pi)]

    Now:
    cos(pi/4) = sin(pi/4) = 1/sqrt(2)
    cos(n*pi) = (-1)^n
    sin(n*pi) = 0

    Thus
    r = (-1)^n*sqrt(2)
    t = pi/4 + n*pi

    -Dan
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