Some Equations for the HP 22S
The [ 2 ] key has the letter X.
These
equations should work for the HP 27S, HP 32S/DM32, or Plus42.
Equations
Answers
are shown to five decimal places.
Snell’s
Law
Equation:
Set Degrees Mode
N ×
SIN(T) = M × SIN(I)
T,
I: reflection angles
N,
M: refractive indices (1 for air, about 1.33 for water, etc.)
Examples:
Inputs:
N = 1, T = 30°, I = 60°, Result: M ≈ 0.57735
Inputs:
N = 1, M = 1.3333, I = 35.4°, Result: T ≈ 50.56589°
Inputs:
N = 1, M = 1.3333, T = 100°, Result: I ≈ 47.61436°
Gudermannian
and Inverse Gudermannian Functions
Equation:
Set Radians Mode
G =
2 × ATAN( TANH( X ÷ 2 ) )
G =
gd(X)
X =
gd^-1(G)
Examples:
Input:
X = 0.5, Result: G ≈ 0.48038
Input:
X = 2.3, Result: G ≈ 1.37095
Input:
G = -0.1, Result: X ≈ -0.10017
Input:
G = 1, Result: X ≈ 1.22619
AC
Current Equation
Equation:
Set Radians Mode
I =
P × SIN( W × T + H )
I =
current at time T seconds in amps
P =
peak current in amps
W =
radian frequency = 2 * π * f
H =
phase angle in radians
Examples:
Inputs:
P = 10, W = 0.8, H = 0, T = 10, Result: I ≈ 9.89358
Inputs:
P = 10, W = 2 * π * 60, H = 0.7, T = 10, Result: I ≈ 6.44218
Inputs:
I = 15, W = 2 * π * 60, H = 0.6, T = 10, Result: P ≈ 26.56548
Air
Pressure Up to 36,089 Feet
Equation:
P =
29.92126 × (1 – 6.875E-6 × H) ^ 5.255876329
H =
height in feet
P =
standard pressure in inHg (inches of Mercury)
The
equation is giving with all the constants calculated.
(see
https://edspi31415.blogspot.com/2024/06/casio-fx-4000p-programs-i-took-on.html
, Prog 8)
Inputs:
H = 1347, Result: P ≈ 28.49332
Inputs:
H = 4126, Result: P ≈ 25.72143
Inputs:
P = 22, Result: H ≈ 8266.49833
Law
of Cosines
SQ(Z)
= SQ(X) + SQ(Y) – 2 × X × Y × COS( C )
SQ:
square function (x^2)
X,
Y, Z = sides
C =
angle that correspond to side Z
Examples:
Inputs:
X = 10, Y = 12, C = 30°
Result:
Z ≈ 6.01281 or Z ≈ 14.38679 (depending on the initial guess
for Z)
Inputs:
X = 55.44, Y = 37.85, Z = 62.17
Result:
C ≈ 81.21305°
Ellipse
Equation
The
center of the ellipse is set at (0, 0).
Equation:
SQ(X
÷ A) + SQ(Y ÷ B) = 1
If A
= B, we are working with a circle.
Examples:
Inputs:
A = 5, B = 5, X = 4.9,
Result:
Y ≈ 0.99499 (1 as a guess)
or Y
gives a no solution error (0 as a guess)
(Your
mileage may vary)
Inputs:
A = 10, X = 8, Y = 12, Result: B = 20
Inputs:
A = 10, X = -4, Y = 6
Result:
B ≈ 6.54654 (10 as a guess)
but
returns a divide by zero error for other guesses (20)
To
store an initial guess on the HP 22S, be out of equation mode and
store the guess in the variable you are trying to solve for.
Eddie
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original content copyright, © 2011-2024. Edward Shore.
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