Convert this rectangular coordinate system point to spherical coordinate system

[skyturnred]

Homework Statement

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

Homework Equations

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!

 

[chrisbaird]

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