Fun with HP 12C Part II
Sine Approximation
Source: Ted’s Math
World, Calculator Magic #4
Retrieved 20141013
sin x ≈ (((x^2/72 – 1)*x^2/42 + 1)*x^/20 – 1)*x^2/6 +
1)*x
STEP

KEY

CODE

STEP

KEY

CODE

01

STO 0

44, 0

21

0

0

02

2

2

22

÷

10

03

y^x

21

23

*

20

04

ENTER

36

24

1

1

05

ENTER

36

25



30

06

ENTER

36

26

X<>Y

34

07

7

7

27

6

6

08

2

2

28

÷

10

09

÷

10

29

*

20

10

1

1

30

1

1

11



30

31

+

40

12

X<>Y

34

32

RCL 0

45, 0

13

4

4

33

*

20

14

2

2

34

STO 1

44, 1

15

÷

10

35

GTO 00

43, 33, 00

16

*

20




17

1

1




18

+

40




19

X<>Y

34




20

2

2




Examples:
sin 0.25 ≈ 0.2474
sin 1.82 ≈ 0.9691
Cosine Approximation
Source: Ted’s Math
World, Calculator Magic #4
Retrieved 20141013
cos x ≈ (((x^2/56 – 1)*x^2/30 + 1)*x^2/12 – 1)*x^2/2 + 1
Registers: R0 = x
in radians, R1 = cos x
STEP

KEY

CODE

STEP

KEY

CODE

1

STO 0

44, 0

17

1

1

2

2

2

18

+

40

3

Y^X

21

19

X<>Y

34

4

ENTER

36

20

1

1

5

ENTER

36

21

2

2

6

ENTER

36

22

÷

10

7

5

5

23

*

20

8

6

6

24

1

1

9

÷

10

25



30

10

1

1

26

X<>Y

34

11



30

27

2

2

12

X<>y

34

28

÷

10

13

3

3

29

*

20

14

0

0

30

1

1

15

÷

10

31

+

40

16

*

20

32

STO 1

44, 1




33

GTO 00

43,33,0







cos 0.33 ≈ 0.23847605343
cos 0.58 ≈ 0.83646264991
Rough Approximation for erf(x)
If x ≤ 1, accuracy is at least 3 digits. Method: 3/8 Integration Rule
Source: Ball, John
A. “Algorithms for RPN Calculators” John Wiley
& Sons: 1978.
STEP

KEY

CODE

STEP

KEY

CODE

1

STO 0

44, 0

26

CHS

16

2

3

3

27

e^x

43, 22

3

÷

10

28

+

40

4

2

2

29

8

8

5

Y^X

21

30

÷

10

6

CHS

16

31

3

3

7

e^x

43, 22

32

*

20

8

ENTER

36

33

RCL 0

45, 0

9

RCL 0

45, 0

34

*

20

10

2

2

35

3

3

11

*

20

36

÷

10

12

3

3

37

1

1

13

÷

10

38

.

48

14

2

2

39

1

1

15

Y^X

21

40

2

2

16

CHS

16

41

8

8

17

e^x

43, 22

42

3

3

18

+

30

43

7

7

19

3

3

44

9

9

20

*

20

45

7

7

21

1

1

46

*

20

22

+

40

47

GTO 00

43,33,00

23

RCL 0

45, 0




24

2

2




25

Y^X

21




Examples:
x = .15; Result ≈
0.1680
x = .50; Result ≈
0.5205
x = 1.25; Result ≈ 0.9220
(actual ≈ 0.9229)
This blog is property of Edward Shore, 2014.
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