Casio
fx-3650P: Chebyshev
Polynomials, Roots of a Complex Number, Reversion Value, Mach Speed,
Trapezoid Perimeter
Chebyshev
Polynomials of the First Kind
Values
of the Chebyshev polynomials can calculated by the following:
T_n
(x):
cos
(n acos x) if |x| ≤ 1
cosh
(n acosh x) if x ≥ 1
(-1)^n
cosh (n acosh(-x)) if x ≤ 1
Inputs:
x, y (n) order. The program assumes y is an integer.
Program
(74 bytes):
?
→ X : ? → Y : X > 1 ⇒ Goto 1 :
-1
> X ⇒ Goto 2 : cos ( Y cos¹ X ) → A : Goto 3 :
Lbl
1 : cosh ( Y cosh¹ X ) → A : Goto 3
Lbl
2 : (-1)^Y * cosh ( Y cosh¹ X ) → A :
Lbl
3: A
Examples
T_Y(X)
X:
-3, Y: 5, Result: -3363
X:
0.3, Y: 5, Result: 0.99888
X:
3, Y: 5, Result: 3363
Roots
of a Complex Number
This
program calculates the roots of a complex number (x + yi)^a, which is
calculated as:
where
k = 0 to n-1
r
=√(x^2 + y^2)
θ
= angle(x + yi) = atan(y/x)
Program
(66 bytes):
?
→ X : ? → Y : ? → A : 0 → M :
Rad
: Pol(X,Y) : A x√ X → B :
Y
→ D : Lbl 1 : M ⊿ Rec(B, (D + 2 π M )/A) ⊿
Y
⊿ 1 M+ : M ≠ A ⇒ Goto 1 : M
The
program stops when M = A.
Example:
(-2
+ 4i)^(1/4)
X:
-2, Y: 4, A: 4
(Fix
4 setting)
M:
0, X: 1.2701, Y: 0.7082
M:
1, X: -0.7082, Y: 1.2701
M:
2, X: -1.2701, Y: -0.7082
M:
3, X: 0.7082, Y: -1.2701
M:
4 (end)
Business:
Reversion Value
Input:
A
= n: number of payments
B
= I%: periodic interest rate (in decimal)
C
= monthly rent
D
= asking price
Note:
For monthly payments, divide the annual interest rate by 1200.
Program
(55 bytes):
Fix
2 : ? → A : ? → B : ? → C : ? → D :
-C
(1 + B) ( (1 + B)^A -1 ) ÷ B → X :
X
+ D (1 + B)^A → X : X
Example:
5
years of monthly payments, A = 60
Interest
rate, B = 6/1200
Monthly
Rate, C = 1895
Asking
Price, D = 250000
Result:
204337.26
Source:
Roger
F. Farish and Elbert B. Greynolds, Jr., Ph.D., CPA Calculator
Analysis for Business and Finance
Texas Instruments Incorporated 1978 ISBN 0-07-063757-1
Mach
Speed
This
program calculates the mach speed, a ratio of the speed of sound
given:
A
= the altitude of the object, such
as a vehicle (in feet)
B
= temperature (°F)
C
= velocity of the vehicle (mph)
Equations
used:
Mach
Number = velocity of the vehicle / speed of sound
where
Speed of Sound = 44100 / 1519 * √( 459.7 + B – 3.57 * A / 1000)
Program
(52 bytes):
?
→ A : ? → B : ? → C :
44100
÷ 1519 * √ ( 459.7 + B – 3.57 A ÷ 1000 ) → D :
C
÷ D → M
A
lapse rate of -3.57° per 1000 ft altitude is assumed.
Example:
Input:
A:
altitude = 2500 ft
B:
temperature = 63 °F
C:
velocity = 795 mph
Result:
mach
speed: 1.208091501
Source:
“Mach
Number and Airspeed vs Altitude” Granite Island Group (Technical
Surveillance Counter Measures) http://www.tscm.com/mach-as.pdf
Retrieved January 26, 2019
Perimeter
of a Trapezoid
P
+ A + B + C * (1/sin X + 1/sin Y)
Program
(38 bytes):
Deg
: ? → A : ? → B : ? → C : ? → X : ? → Y :
A
+ B + C ( 1 ÷ sin X + 1 ÷ sin Y )
Example:
A
= 227.6
B
= 305.4
C
= 10.5
X
= 86°
Y
= 5°
Result:
663.999629
Eddie
All
original content copyright, © 2011-2019. Edward Shore.
Unauthorized use and/or unauthorized distribution for commercial
purposes without express and written permission from the author is
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