Spherical Coordinates of a Point with Rectangular Coordinates

[xzibition8612]

Homework Statement

Find the spherical coordinates of the point with rectangular coordinates (2√2, -2√2, -4√3)

Homework Equations

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The Attempt at a Solution

The textbook gives the answer as (8, -pi/4, 5pi/6)
No idea how to get to this. Any help appreciated.

 

[FanofAFan]

so you need to find $$\rho$$ $$\theta$$ and $$\varphi$$ and you are given (x,y,z) so we know $$\rho$$² = x^2 + y^2 +z^2 and you get $$\theta$$ from thinking of the graph on the xyz plane and $$\theta$$ runs on the xy plan and -2$$\sqrt{2}$$ is from SOH CAH TOA and realizing its just negative 45 degrees ie 45 ($$\pi$$/180) =??

 

[I like Serena]

Here's the set of formulas that define the transformation:

Note that in the textbook answer the angles have been exchanged.
For the proper set of formulas you should have defined how the polar coordinates have been defined in your textbook. Is expect that your textbook will mention a similar set of formulas.