Saturday, July 14, 2012

Programs for HP 48S and What's Coming Up

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^2-2BC 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 Mier-Jedrzejowicz 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 TI-84 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

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