Iterating a Rotation

★ 6/10functions trigonometry Trigonometric Identities Induction

Problem

Let $\theta$ be a constant, and define a sequence of functions by

f_1(x) = \frac{x\cos\theta - \sin\theta}{x\sin\theta + \cos\theta}, \qquad f_{n+1}(x) = f_1(f_n(x)), \quad n \in \mathbb{N}.

Find $f_{2021}(x)$ .

Answer

Solution

Difficulty	6/10
Topics	functions, trigonometry, Trigonometric Identities, Induction

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