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Math Help - spherical and cyndrical coordinates?

  1. #1
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    Question spherical and cylindrical coordinates?

    I have 2 problems that i am stuck on

    1) Find a set of cylindrical coordinates (with r ≥ 0 and 0 ≤ θ < 2π) of the point whose Cartesian coordinates are given. (-5, -5, -4)

    i have already found r and z, which are (5sqrt(2), ? ,-4) and have confirmed that those 2 are correct but i cannot find the right answer for theta.

    This is what i have tried but it is not the correct answer and i do not know why.

    y/x=tan(theta)
    theta = arctan(-5/-5)
    theta = arctan(1) = pi/4 (wrong?!?!?! why?!?!)


    2) Find a set of spherical coordinates (with ρ ≥ 0, 0 ≤ ϕπ and 0 ≤ θ < 2π) of the point whose Cartesian coordinates are given.(0, 5√3, 5)

    On this one, i already solved for rho and p but not for theta.
    (10, arctan((sqrt(75))/5) , ? )

    This is what i have tried but i dont understand how you can divide by zero.
    tan(theta) = y/x
    theta = arctan(5sqrt(3)/0) (divide by zero?!?! what?!?!)




    Can anyone help? THANKS!!
    Last edited by break; October 19th 2010 at 06:56 PM.
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  2. #2
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    For the first one, if \tan\theta is positive then the angle can be in either the first or third quadrant. You have to look at the context (a diagram ?) to decide which.

    For the second one, \tan90^{\circ}=\infty.
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  3. #3
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    Quote Originally Posted by BobP View Post
    For the first one, if \tan\theta is positive then the angle can be in either the first or third quadrant. You have to look at the context (a diagram ?) to decide which.

    For the second one, \tan90^{\circ}=\infty.
    thanks for helping me figure out the first one! i got 5pi/4

    Also, how did u get infinity for the 2nd one? is it because i divide by zero i automatically assume infinity?
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  4. #4
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    Yes, unless there is a zero on the top line as well. (0/0 is indeterminate).
    But, draw a diagram and you should be able to see what the angle is.
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