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Thread: 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; Oct 19th 2010 at 06:56 PM.
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  2. #2
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    For the first one, if $\displaystyle \tan\theta$ 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, $\displaystyle \tan90^{\circ}=\infty.$
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  3. #3
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    Quote Originally Posted by BobP View Post
    For the first one, if $\displaystyle \tan\theta$ 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, $\displaystyle \tan90^{\circ}=\infty.$
    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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