intercomparing circular and hyperbolic trigonometric functions.

The circular trigonometric identity cos²(u) + sin²(u) = 1 describes each point on the perimeter of the circle x² + y² = 1 as a function of angle u. 

In a sense the hyperbolic trigonometric identity cosh²(u) - sinh²(u) = 1 mimics this approach by substituting x² - y² = 1 as a function of hyperbolic sector u.