It is assumed that (x) is always ≥ 1 and the (1/x) is always ≤ 1.
The ‘cosmic’ equation
Linking the ‘cosmic’ equation with Pythagoras.
Linking the ‘cosmic’ equation with trigonometry and the trigonometric functions.
Simplifying the tan relationship.
more stuff
more stuff
The Triangles
The relationship between the red and blue triangles.
More stuff.
Example A
Visualising the triangles using the ‘cosmic’ equation.
Substituting x₁ (from above) into the green triangle.
Scale by x₁ and substitute cos. Using circles to perform square-roots (more information).
Example B
More stuff.
And then..
Mathematics Dude 