# Thread: spherical and cyndrical coordinates?

1. ## 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!!

2. 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, $\displaystyle \tan90^{\circ}=\infty.$

3. Originally Posted by BobP
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?

4. 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.