01-08-2016, 03:24 AM
Link:
http://edspi31415.blogspot.com/2016/01/h...nd-2d.html
HP 15C: Digital Root
Input: Enter an integer and execute Label A (or whatever label you want to assign).
Program:
Formula used: (Define DR(n) as the digital root function)
DR(n) = n – 9 * int((n-1)/9), n > 0
DR returns the sum of n’s digits and repeats until a single digit remains.
Examples:
DR(4514) = 5
DR(9376) = 7
DR(636088) = 4
DR(761997) = 3
HP 15C: Modulus Function
Input:
Y: A
X: B
The program calculates A mod B.
Program:
Formula Used:
A mod B = B * frac(A/B)
Add B to result if A*B < 0.
Registers Used:
R1 = A
R2 = B
R3 = A mod B
Examples:
A = 48, B = 3, result = 0
A = 41.3, B = 12, result = 5.3
A = 48, B = -7, result = -1
A = -50.2, B = 36, result = 21.8
HP 15C: 2D Coordinate Rotation
Input: Store the following: X in R4, Y in R5, and θ in R3. Run the program.
Results are stored in R6 and R7, for X’ and Y’, respectively. X’ is displayed first, press R/S to get Y’.
This program uses the Polar to Rectangular conversion.
Program:
Formulas Used:
X’ = X * cos θ – Y * sin θ
Y’ = X * sin θ + Y * cos θ
Examples:
X (R4) = 1, Y (R5) = 2, θ (R3) = 30°. Results: X’ (R6) ≈ -0.1340, Y’ (R7) ≈ 2.2321
X (R4) = 6.45, Y (R5) = 5.25, θ (R3) = 176°. Results: X’ (R6) ≈ -6.8005, Y’ (R7) ≈ -4.7872
http://edspi31415.blogspot.com/2016/01/h...nd-2d.html
HP 15C: Digital Root
Input: Enter an integer and execute Label A (or whatever label you want to assign).
Program:
Code:
Step Key Key Code
001 LBL A 42, 21, 11
002 ENTER 36
003 ENTER 36
004 1 1
005 - 30
006 9 9
007 ÷ 10
008 INT 43, 44
009 9 9
010 * 20
011 - 30
012 RTN 43, 32
Formula used: (Define DR(n) as the digital root function)
DR(n) = n – 9 * int((n-1)/9), n > 0
DR returns the sum of n’s digits and repeats until a single digit remains.
Examples:
DR(4514) = 5
DR(9376) = 7
DR(636088) = 4
DR(761997) = 3
HP 15C: Modulus Function
Input:
Y: A
X: B
The program calculates A mod B.
Program:
Code:
Step Key Key Code
001 LBL B 42, 21, 2
002 STO 2 44, 2
003 X<>Y 34
004 STO 1 44, 1
005 X<>Y 34
006 ÷ 10
007 FRAC 42, 44
008 RCL* 2 45, 20, 2
009 STO 3 44, 3
010 RCL 1 45, 1
011 RCL* 2 45, 20, 2
012 TEST 1 (x > 0) 43, 30, 1
013 GTO 1 22, 1
014 RCL 3 45, 3
015 RCL+ 2 45, 40, 2
016 STO 3 44, 3
017 RTN 43, 32
018 LBL 1 42, 21, 1
019 RCL 3 45, 3
020 RTN 43, 32
Formula Used:
A mod B = B * frac(A/B)
Add B to result if A*B < 0.
Registers Used:
R1 = A
R2 = B
R3 = A mod B
Examples:
A = 48, B = 3, result = 0
A = 41.3, B = 12, result = 5.3
A = 48, B = -7, result = -1
A = -50.2, B = 36, result = 21.8
HP 15C: 2D Coordinate Rotation
Input: Store the following: X in R4, Y in R5, and θ in R3. Run the program.
Results are stored in R6 and R7, for X’ and Y’, respectively. X’ is displayed first, press R/S to get Y’.
This program uses the Polar to Rectangular conversion.
Program:
Code:
Step Key Key Code
001 LBL C 42, 21, 13
002 RCL 3 45, 3
003 RCL 4 45, 4
004 >R 42, 1
005 STO 6 44, 6
006 X<>Y 34
007 STO 7 44, 7
008 RCL 3 45, 3
009 RCL 5 45, 5
010 >R 42, 1
011 RCL 7 45, 7
012 + 40
013 STO 7 44, 7
014 X<>Y 34
015 CHS 16
016 RCL 6 45, 6
017 + 40
018 STO 6 44, 6
019 R/S 31
020 X<>Y 34
021 RTN 43, 32
Formulas Used:
X’ = X * cos θ – Y * sin θ
Y’ = X * sin θ + Y * cos θ
Examples:
X (R4) = 1, Y (R5) = 2, θ (R3) = 30°. Results: X’ (R6) ≈ -0.1340, Y’ (R7) ≈ 2.2321
X (R4) = 6.45, Y (R5) = 5.25, θ (R3) = 176°. Results: X’ (R6) ≈ -6.8005, Y’ (R7) ≈ -4.7872