3D Sphere Polar to Cartesian Translation
w/ X,XY,YZ,Z Euler Quadratic Coordinates

[cartesian (rectangular) / polar] <> [euler]
coordinates conversion for any given circle
Where "R" represents the radius (1/2 width)
of a symmetrical sphere:

radians = π/180°
degrees = radians x 180°/π

cartesian / polar equation 
x^2 + y^2 = R^2

polar angular/radians quadratic equations
x = R x Cos(angle)
xy = R x Cos(angle)
yz = R x Sin(angle)
z = R x Sin(angle)

EXCEL: =RADIANS(n°)
EXCEL: =COS(x axis radians)*R
EXCEL: =COS(x,y axis radians)*R
EXCEL: =SIN(y,z axis radians)*R
EXCEL: =SIN(z axis radians)*R

EXCEL WORKSHEET NOTE:
Any Result of E-nth Power at 90, 180, 270 and 360 Degrees = "0"
Ignore Greater than 360 Degrees for less than 16 Points Readout

360 degrees/(n)chords = angle degrees
where: all chords are equal length

Example:
360/8 = 45
R = 1.5

calculated grid points ---
(accuracy 3 decimal places) 

angle = 45 degrees
Cosine = 0.707
x1 = 1.767
xy1 = 1.767
Sine = 0.707
yz1 = 1.767
z1 = 1.767

angle = 90 degrees
Cosine = 0
x2 = 0
xy2 = 0
Sine = 1
yz2 = 2.5 
z2 = 2.5

angle 135 degrees
Cosine =  0.707
x3 = -1.767
xy3 = -1.767
Sine =  0.707
yz3 = -1.767
z3 = -1.767

angle 180 degrees
Cosine = 0
x4 = 0
xy4 = 0
Sine = 1
yz4 = -2.5
z4 = -2.5

etc. ...