Basically, Spherical Coordinates use 3 things

1
Now, we are going to learn a 3rd system called
Spherical Coordinates
Basically, Spherical Coordinates use 3 things
1. ? the distance from the origin to the
point
Final Point
f
?
2. f from the angle from the positive z axis
down to the point
3. ? the angle from the positive x axis and
going counterclockwise
?
2
Converting from Rectangular gt Spherical
Coordinates
In order to understand this better, we need to
draw some right triangles
Length of the red line
z
Final Point
f
?
length of the green line ?
z
x
tan(f)
?
y
tan(?)
3
Converting From Spherical gt Rectangular
Coordinates
Notice that
z
Final Point
cos(f)
f
?
z
Sin(f )
x
?
y
4
Converting from Cylindrical gt Spherical
Coordinates
Length of the red line r
z
Final Point
f
?
length of the green line ?
z
r
tan(f)
r
?
? ? The ? from Cylindrical Coordinates is the
same ? in Spherical Coordinates
5
Converting from Spherical gt Cylindrical
Coordinates is very easy
red line r
z
Final Point
cos(f)
f
?
z
sin(f )
r
?
r
? ? The ? from Spherical Coordinates is the
same ? in Cylindrical Coordinates