## 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 + x2 * (0.00761 * x2 - 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 + x2 * (0.03705 * x2 - 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