## Friday, May 16, 2014

### fx-5800p Programs (can apply to Casio graphing calculators also, e.g. fx-9860g, Prizm)

This is a collection of programs I wrote on the Casio fx-5800p. These programs should also work on any Casio Graphing calculator (fx-9860g, fx-9750g, Prizm) since the programming language between Casio calculators remains largely the same.

Now if I can find my fx-5800p that I misplaced last night... *sigh*. Thank goodness for notes!

Notes for the fx-5800p programs:

There are no SIGN or MOD functions. Here are the work arounds I used (see SUN):

SIGN(x):
...
X > 0 ⇒ 1 → X
-X > 0 ⇒ -1 → X
...

n MOD d:
...
N - D Intg( N ÷ D ) → result variable
....

1. Rotation of (x, y) (ROTATEXY)
2. Law of Cosines (COSINES)
3. Pendulum: Period and Average Velocity (PENDULUM)
4. Arc Length of a Parabola (QUADLENGTH)
5. Position of the Sun (SUN)

1. fx-5800p: ROTATEXY

Rotates the coordinate (X, Y). The direction of rotation follows the conventional direction (counterclockwise). The variable A represents the angle (θ).

Program:
"X"? → X
"Y"? → Y
"ANGLE"? → A
[ [ X, Y ] ] × [ [ cos(A), sin(A) ] , [ -sin(A), cos(A) ] ]

2. fx-5800p: COSINES

Sides: D, E, F
Corresponding Angles: A, B, C

Program:
Lbl 0
Cls
"KNOWN:"
"1. D,E,F"
"2. A,E,F"
?→I
I = 1 ⇒ Goto 1
I = 2 ⇒ Goto 2
Goto 0
Lbl 1
"D"? → D : "E"? → E : "F"? → F
"A" : cos ⁻¹ (( E ² + F ² - D ² ) ÷ ( 2EF )) → A ◢
"B": cos ⁻¹ (( D ² + F ² - E ² ) ÷ ( 2DF )) → B ◢
"C" : 180° - A - B
Stop
Lbl 2
"A"? → A : "E"? → E : "F"? → F :
"D": √ (E ² + F ² - 2 E F cos A ) → D ◢
"B" : cos ⁻¹ ( ( D ² + F ² - E ² ) ÷ (2DF)) → B ◢
"C": 180° - A - B

3. fx-5800p: PENDULUM

Variables:
D = length of the step or bar holding the pendulum
L = length of the rod or string that is swinging
R = large radius of the circular ring

At the units, enter 0 for US units (set g = 32.174 ft/s^2), anything else for SI units (g = 9.80665 m/s^2).

Calculated:
T = period of the pendulum (the amount of time it takes for the pendulum from one end to the other)
V = average velocity of the pendulum (once in its in full swing)

Program:
Cls
"=0 U.S."
"≠0 SI"
? → G
If G = 0
Then 32.174 → G
Else g → G IfEnd // g from the constant menu (9.80665)
Lbl 0
Cls
"1. ROD 2. STRING"
"3. RING"
?→ I
I = 1 ⇒ Goto 1
I = 2 ⇒ Goto 2
I = 3 ⇒ Goto 3
Goto 0
Lbl 1
"D"? → D : "L"? → L
2 π √( L ÷ 3G ) → T : Goto 4
Lbl 2
"D"? → D : "L"? → L
2 π √(L ÷ G) → T : Goto 4
Lbl 3
"D"? → D : "L"? → L : "R"? → R
2 π √( R ² ÷ GL → T : Goto 4
Lbl 4
"T =" : T ◢ "V =": D ÷ T → V

-----

Test Examples:

Rod: D = 1 m, L = 1.6 m. Results: T = 14.36943096 sec, V = .0695921782 m/s

String: D = 2 m, L = 1.75 m. Results: T = 2.65423008 sec, V = .07535141995 m/s

Circular Ring: D = 2 ft, L = 2 ft, r = 1.2 ft
Results: T = 1.879851674 sec, V = 1.063913727 m/s

Find the length of a parabola given height and width and a corresponding equation:

f(x) = Ax^2 + Bx

Where
A = -4h/l^2
B = 4h/l

Program:
Cls
"LENGTH"? → L
"HEIGHT"? → H
Cls
"COEF OF X ²"
-4 H ÷ L ² ◢
"COEF OF X"
4 H ÷ L ◢
"ARC LENGTH"
∫ ( √ ( 1 + ( -8 H X ÷ L ² + 4 H ÷ L ) ) , 0, L)

Test Data:
L: 16.4, H: 8.2
X^2 coefficient: -.1219512195
X coefficient: 2

5. fx-5800P: SUN

Source for the formulas: http://aa.usno.navy.mil/faq/docs/SunApprox.php

Gives the RA (right ascension) and δ (declination) of the sun at any date. U is the universal time, the time it would be at Greenwich Village (Int'l Date Line).

For the Pacific Time Zone:
Standard Time: PST + 8 hours = UT
Daylight Savings Time: PDT + 7 hours = UT

Program:
"MONTH"? → M
"DAY?" → D
"YEAR"? → Y
"UNIV. TIME"? → U
Deg
100 Y + M - 190002.5 → X
X > 0 ⇒ 1 → X
-X > 0 ⇒ -1 → X
367 Y - Intg( 7 ( Y + Intg( ( M + 9 ) ÷ 12 ) ) ÷ 4 )
+ Intg( 275 M ÷ 9 ) + D + 1721013.5 + U ÷ 24
- .5 X + .5 → D
D - 2451545 → D
357.529 + .98560028 D → G
G - 360 Intg( G ÷ 360 ) → G
280.459 + .98564736 D → Q
Q - 360 Intg( Q ÷ 360 ) → Q
Q + 1.915 sin( G ) + .02 sin( 2G ) → L
L - 360 Intg( L ÷ 360 ) → L
1.00014 - .01671 cos( G ) - .00014 cos( 2 G ) → R
23.439 - .00000036 D → E
tan ⁻¹ (cos(E) tan(L)) → A
If L ≥ 90 And L < 270
Then A + 180 → A
IfEnd
If L ≥ 270 And L < 360
Then A + 360 → A
IfEnd
A ÷ 15 → A
sin ⁻¹ ( sin(E) sin(L) ) → C
"APPROX:"
"RA (HRS)": A ◢
"DEC (DEG)": C

Test Data:
M: 5
D: 14
Y: 2014
U: 19

RA: 3.43 hours
DEC: 18.746°

Eddie

This blog is property of Edward Shore. 2014

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