HP 48: Law of Sines and Cosines, Quadratic Formula, and Cubic Formula.
Hi everyone! Recently, a poster on the MoHPC HP Calculator Forum asked for programs for solving triangles and finding roots for polynomials. (link here)
I will repost the programs here. They have been done with the HP 48S.
Law of Sines:
sin(θ1)/S1 = sin(θ2)/S2. Apply this to any of the two sides and their corresponding angels.
θ which can be typed by pressing:
HP 48S: [alpha] [right shift] (F)
HP 48G: [alpha] [right shift] (F)
HP 50g: [alpha] [right shift] (T)
LAWSIN:
<< 'SIN(θ1)/S1=SIN(θ2)/S2' STEQ 30 MENU>>
Law of Cosines:
A^2=B^2+C^22BC cos θ
LAWCOS:
<< 'SQ(A)=SQ(B)+SQ(C)2*B*C*COS(θ)' STEQ 30 MENU>>
30 MENU brings up the calculator's solver using whatever is stored in STEQ.
QD: (Quadratic Formula)  Credit goes to the document "1 Minute Marvels" by Wldoek MierJedrzejowicz and Richard Nelson (They have this program named 'quad')
Input:
3: A
2: B
1: C
Output:
2: root 1
1: root 2
<< 3 PICK / SWAP ROT 2 * / DUP SQ ROT  √ + LASTARG  >>
SQRT: Square Root
CU: Cubic Formula Uses the program QD above. This program finds the roots of AX^3+BX^2+CX+D=0
Input:
4: A
3: B
2: C
1: D
Output:
3: root 1
2: root 2
1: root 1
Program:
<< → A B C D
<<
C 3 A * / B SQ 9 A SQ * /  'Q' STO
C B * A SQ / 3 D * A /  6 / B 3 ^ 27 A 3 ^ * /  'R' STO
R Q 3 ^ R SQ + √ + 3 XROOT 'S' STO
R Q 3 ^ R SQ + √  3 XROOT 'T' STO
S T + B 3 A * /  'X' STO
X
B A X * +
C B X * + A X SQ * +
QD
{Q,R,S,T,X} PURGE >> >>
What is Coming Up
Coming in August, I will do a short series which I will use a graphing calculator with programming capabilities, most likely the TI84 Plus, to demonstrate how programming is used to assist in mathematical applications: including finding the amount of miles between two places, projectile motion, and random walks.
If you get a chance, check out the Math/Maths Podcast. Link: Pulse Project
Until then,
Eddie
This blog is property of Edward Shore. © 2012
A blog is that is all about mathematics and calculators, two of my passions in life.
Saturday, July 14, 2012
Programs for HP 48S and What's Coming Up
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