Sine Functions on 4K

You can closely approximate sine functions on your 4K ROM with a few BASIC statements.

These equations simulate sine between 0 and 45° (X in integer degrees):

1000sin(X)=[ 2621X - 11X² - 11X³ ]/10
             -----   ----   ----
              15     450    1350

Program sine using:

R=(11*X**2)/450+((11*X**2)/1350)*X
S=(262*X)/15-R/10

where S is 1000 times sin(X).

---

Lori Olson added this note to her sine and cosine programs. To approximate tangent with 4K ROM, use this equation:

   1000tan(X)=1000sin(X)
                  cos(X)

Program tangent using:

LET T=(25*S)/(C/40)

where S=1000sin(X), C=1000cos(X). (See p.2 & p.16 for sin and cos.) The error increases with X and any X>88 produces an overflow.