u/DotBeginning1420

I'm not sure I got this right.

We have:

A_1 = sin(𝜃)
B_1 = cos(𝜃)

For every n > 1:

A_n = A_(n-1) - B_(n-1)
B_n = A_(n-1) + B_(n-1)

We need to find an iterative expression for A and B.

>!I got that:!<

>!--------------------------------------------/ sin(𝜃) n mod 4 = 1!<
>!------------------------------------------/ sin(𝜃-𝜋/4) n mod 4 = 2!<
>!A_n = (-1)^⌊(n+1)/4⌋ ∙ (√2)^(n-1) ∙ 〈 !<
>!------------------------------------------\ cos(𝜃) n mod 4 = 3!<
>!-------------------------------------------\ cos(𝜃-𝜋/4) n mod 4 = 0!<

>!-------------------------------------------/ cos(𝜃) n mod 4 = 1!<
>!-----------------------------------------/ cos(𝜃-𝜋/4) n mod 4 = 2!<
>!B_n = (-1)^⌊(n-1)/4⌋ ∙ (√2)^(n-1) ∙〈!<
>!-----------------------------------------\ sin(𝜃) n mod 4 = 3!<
>!------------------------------------------\ sin(𝜃-𝜋/4) n mod 4 = 0!<

>!Sorry if it looks too complicated. Do we have to use Modulo and Floor to express the seemingly periodic behavior of these funcitons?!<