## HP12c software: Sine and Cosine approximations

As an engineer I should really only be using the HP15c but sometimes
I use as well a HP12c. The HP12c has no trigonometric functions.
It is however possible to use the following approximations and write
a short hp12c program.
### sin approximation

sin(x) = x * ( 1 + x^{2} * (0.00761 * x^{2} - 0.16605))
x must be between 0 and π/2
Error of the approximation: 2 * 10^{-4} for 0 <= x <= pi/2

### cos approximation

cos(x) = 1 + x^{2} * (0.03705 * x^{2} - 0.49670))
x must be between 0 and π/2
Error of the approximation: 2 * 10^{-9} for 0 <= x <= pi/2
It is as well possible to use this formula:
cos(x) = sqrt(1 - sin(x)^{2}) for 0 <= x <= pi/2

### tan

tan(x) = sin(x)/cos(x) = sin(x)/(sqrt(1 - sin(x)^{2}))

### A sin(x) program

command display
f PRGM 00- (to delete any existing program)
STO 9 01- 44 9
Enter 02- 36
* 03- 20
. 04- 48
0 05- 0
0 06- 0
7 07- 7
6 08- 6
1 09- 1
* 10- 20
. 11- 48
1 12- 1
6 13- 6
6 14- 6
0 15- 0
- 17- 30
RCL 9 18- 45 9
* 19- 20
RCL 9 20- 45 9
* 21- 20
1 22- 1
+ 23- 40
RCL 9 24- 45 9
* 25- 20
now press f P/R to leave
the programming mode

This program uses the following register: STO 9

### Using the program

Just enter the angle in RAD (fractions of π=3.14159) and then press
R/S.

Example for x = 45°= 3.14159/4:
To calculate sin(x) type R/S and the result should be 0.7072

### References

© Guido Socher