Spherical coordinates conversion?

[whig4life]

The point P has Cartesian coordinates (√2,1,1). Find the spherical coordinates of P.

I watched several videos on this on Youtube, and I seem to be missing something because they arrive at an answer I am wondering how they got there. Can anyone explain how to arrive at the answer for this? Thank you

 

[srmichael]

The point P has Cartesian coordinates (√2,1,1). Find the spherical coordinates of P.

I watched several videos on this on Youtube, and I seem to be missing something because they arrive at an answer I am wondering how they got there. Can anyone explain how to arrive at the answer for this? Thank you

This may explain it in a different way that may make more sense:

http://www.math.montana.edu/frankw/ccp/multiworld/multipleIVP/spherical/learn.htm

 

[whig4life]

That website was really helpful.

So here's my attempt so far:

I got P= 2 and Φ= π/3 and θ= arcsin(1/√3)

θ is my only problem left, what is the mathematically appropriate expression for this on the (P,θ, Φ) form?