A Rotating Recurrence Pair

★ 7/10complex numbers trigonometry Geometric Progression sequences Trigonometric Identities

Problem

Real sequences $\{a_n\}$ and $\{b_n\}$ (all terms nonzero) satisfy

\begin{cases}a_n=a_{n-1}\cos\theta-b_{n-1}\sin\theta,\\ b_n=a_{n-1}\sin\theta+b_{n-1}\cos\theta,\end{cases}

with $a_1=1$ , $b_1=\tan\theta$ , where $\theta$ is a given constant. Find the general terms of $\{a_n\}$ and $\{b_n\}$ .

Answer

Solution

Difficulty	7/10
Topics	complex numbers, trigonometry, Geometric Progression, sequences, Trigonometric Identities

Whiteboard

Your sketch is saved only in this browser. To share it, export your drawing as an image (whiteboard menu → Export as → PNG), then upload that image in the comments below.

Discussion

Ask questions, share alternate solutions, and use LaTeX freely.

0 comments

No comments yet.