# Homework Help: Convert this rectangular coordinate system point to spherical coordinate system

1. Mar 30, 2012

### skyturnred

1. The problem statement, all variables and given/known data

The point is (0, -8, 0)
r≥0
0≤θ≤2∏
0≤$\varphi$≤∏

2. Relevant equations

3. The attempt at a solution

So here is what I've done so far:

I know that r=8 because x and z are 0

I know that θ=∏/4 or 3∏/4, but which one? both of these satisfy the following equation (which is the only one I know for this)

cos(θ)=y/x

Also, I am confused about $\varphi$. I know that:

tan($\varphi$)=y/x, but y is negative, and x is zero. I know the value of arctan(∞) as well as arctan(-∞) but which one do I use? I am so confused. Thanks!

2. Mar 30, 2012

### chrisbaird

Draw a diagram and plot your point, then go from there by comparing to this.