Little math problem(s) January 2019

[Thomas Klemm]

(01-28-2019 01:53 AM)Paul Dale Wrote:  As the function approaches zero, the relative error will become controllable.

Here's an HP-42S program that uses this idea to calculate \(sin(1)\approx8.41470984808e-1\):

Code:

00 { 20-Byte Prgm }
01 1
02 SIN
03 RCL- ST Y
04 RAN
05 0.4
06 ×
07 0.8
08 +
09 ×
10 +
11 END

Make sure to use RAD mode.

Example:

0
R/S
8.13930075171e-1
R/S
8.37292640515e-1
R/S
8.41890339484e-1
R/S
8.41404810797e-1
R/S
8.41460042846e-1
R/S
8.41472832565e-1
R/S
8.41470715347e-1
R/S
8.41470956453e-1
R/S
8.41470980231e-1
R/S
8.41470985454e-1
R/S
8.41470984835e-1
R/S
8.41470984811e-1
R/S
8.41470984808e-1
R/S
8.41470984808e-1
…

Cheers
Thomas