Several well-known trigonometric formulas are intimately tied with Fibonacci and Lucas numbers via the trigonometric functions.
For example, a number of interesting relationships exist linking Fibonacci and Lucas numbers with the inverse tangent function , and the ubiquitous irrational number :
26.1 GOLDEN RATIO AND INVERSE TRIGONOMETRIC FUNCTIONS
Several interesting relationships link the golden ratio with inverse trigonometric functions.
Since for , it follows that . Likewise, .
Suppose . Then , so . Since , it follows that , and . Then . In addition, . Br. L. Raphael of ...