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
All original content copyright, © 2011-2024. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
