(12C) Bhaskara's Sine and Cosine Approximations

[Thomas Klemm]

(07-29-2022 05:13 PM)Albert Chan Wrote:  We don't have estimate formula for asin(x), because sin(x) were defined from estimated cos(x)
In other words, OP sin estimate formula is not needed; it is same as cos(90° - x°)

Agreed. Instead we can use:

Code:

01-     43 33 07 g GTO 07
02-     36         ENTER
03-     09         9
04-     00         0
05-     34         x≷y
06-     30         −
07-     06         6
08-     00         0
09-     10         ÷
10-     36         ENTER
11-     20         ×
12-     09         9
13-     34         x≷y
14-     40         +
15-     09         9
16-     43 36    g LSTx
17-     04         4
18-     20         ×
19-     30         −
20-     34         x≷y
21-     10         ÷
22-     43 33 00 g GTO 00

However the jump table is now switched:

GTO 01 for \(\cos(x)\)
GTO 02 for \(\sin(x)\)

Quote:cos(45°) ≈ cos(1/4 ht) = (1-4/16) / (1+1/16) = 12/17 ≈ 0.7059

IIRC I used 9 and 60 instead of 1 and 180 to save one precious step.