Calculator test

[Commie]

(Today 04:48 PM)Albert Chan Wrote:  2000/pi ≈ 636.619772 = 637 - 0.380228

We divide radians by pi, not (2*pi), so that reduced angle is within ±pi/2

sin(pi - x) = sin(x)

asin(sin(2000)) ≈ asin(sin(0.380228*pi)) ≈ asin(0.930040) ≈ 1.19452

637*pi - 1.19452 ≈ 2000.00000

cos(pi - x) = -cos(x)

acos(cos(2000)) ≈ acos(-cos(0.380228*pi)) ≈ acos(-0.367458) = pi - acos(0.367458) ≈ 1.94707

637*pi - (pi - 1.94707) = 637*pi - 1.19452 ≈ 2000.00000

Hi Albert,

First off, I was hoping Naddy or A1 or both could give the answer since they are both very smart guys, sigh...

I do it slightly differently to you, but first let me just mention that the sine algorithm which is either using cordics or poly's in both cases the ranges are limited, usually between -pi/2...pi/2.
So the calculator is reducing the 2000.x to get it in range for the Cordic or poly algorithm.

Assuming x is one then the sine(2000) gives 0.93 and the arcsine(0.93....) gives 1.19452.... but
sine(1.19452...) gives 0.93 now where has the 637*pi gone?
What does the calculator do with it?

I do it slightly different, 2000/(2.pi)=318.3098862, now remove 318 to leave 0.3098862
Then 0.3098862*2.pi=1.947072317 which then goes to the sine poly to yield
sine(2000)=0.9300395044.This commonly known in the trade as removing the sine circles.
Now, I started with 2000 right?, what does the calculator do with the excess sine circles? On any calculator for that matter, because evidently there is a big difference between sine(2000) and sine(1.947072317)? My sine algorithm is limited to just -pi...pi.?

Cheers
Darren