swapped the y and z in latex

Author: trevordblack

books/RayTracingTheNextWeek.html

@@ -1151,23 +1151,23 @@
 unit radius sphere on the origin is:
 
   $$ x = \cos(\phi) \cos(\theta) $$
-  $$ y = \sin(\phi) \cos(\theta) $$
-  $$ z = \sin(\theta) $$
+  $$ z = \sin(\phi) \cos(\theta) $$
+  $$ y = \sin(\theta) $$
 </div>
 
 <div class='together'>
 We need to invert that. Because of the lovely `<cmath>` function `atan2()` which takes any number
-proportional to sine and cosine and returns the angle, we can pass in $x$ and $y$ (the
+proportional to sine and cosine and returns the angle, we can pass in $z$ and $x$ (the
 $\cos(\theta)$ cancel):
 
-  $$ \phi = \text{atan2}(y, x) $$
+  $$ \phi = \text{atan2}(z, x) $$
 </div>
 
 <div class='together'>
 The $atan2$ returns values in the range $-\pi$ to $\pi$, so we need to take a little care there.
 The $\theta$ is more straightforward:
 
-  $$ \theta = \text{asin}(z) $$
+  $$ \theta = \text{asin}(y) $$
 
 which returns numbers in the range $-\pi/2$ to $\pi/2$.
 </div>