MattRob
- 208
- 29
So, I was curious about this and found more or less what I was looking for here: http://electron9.phys.utk.edu/vectors/3dcoordinates.htm
Except, something is bothering me about those equations. At the very bottom, the equation for Theta in a spherical coordinate system; shouldn't it be
\theta = {tan^{-1}}( \frac{\sqrt{{x^{2}}+{y^{2}}}}{z})
instead of
\theta = {tan^{-1}}( \frac{z}{\sqrt{{x^{2}}+{y^{2}}}})
(The image in question)
Because {tan^{-1}}( \frac{opposite}{adjacent}) = \theta , and looking at angle \theta , the line opposite of it is exactly equal to \sqrt{{x^{2}}+{y^{2}}} , and the line adjacent to it equal to z.
So I'm wondering if I'm in error (and how so if I am) or if the linked page is.
Except, something is bothering me about those equations. At the very bottom, the equation for Theta in a spherical coordinate system; shouldn't it be
\theta = {tan^{-1}}( \frac{\sqrt{{x^{2}}+{y^{2}}}}{z})
instead of
\theta = {tan^{-1}}( \frac{z}{\sqrt{{x^{2}}+{y^{2}}}})
(The image in question)
Because {tan^{-1}}( \frac{opposite}{adjacent}) = \theta , and looking at angle \theta , the line opposite of it is exactly equal to \sqrt{{x^{2}}+{y^{2}}} , and the line adjacent to it equal to z.
So I'm wondering if I'm in error (and how so if I am) or if the linked page is.