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FIBONOMETRY I

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 c026-math-001, and the ubiquitous irrational number c026-math-002:

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26.1 GOLDEN RATIO AND INVERSE TRIGONOMETRIC FUNCTIONS

Several interesting relationships link the golden ratio with inverse trigonometric functions.

Since c026-math-003 for c026-math-004, it follows that c026-math-005. Likewise, c026-math-006.

Suppose c026-math-007. Then , so . Since , it follows that , and . Then . In addition, . Br. L. Raphael of ...

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