Tuesday, March 14, 2023

Casio Classpad (fx-CP400): Collection of Functions

Casio Classpad  (fx-CP400):  Collection of Functions



For my birthday post, on Pi (π) Day (March 14), here is a collection of functions for the Casio Classpad (300, 330, fx-CP400, fx-CP500). 



Birthday Probability Function:   bday(c,n)


"The probability that a number in a room do not share a same birthday"

c:  number of categories (i.e. days in a year)

n:  population size


Example:

bday(365, 40):  0.1087681902



Percent Change:  pchg(old, new)


old:  old amount

new:  new amount


Example:

pchg(400,500):  25



Combination with Repetition:  nHr(n,r)


n:  population

r:  number of objects to pick


Example:

nHr(52,5):  3819816



Error Function and Error Compliment Function


Error Function:   erf(x)

Error Compliment Function:  erfc(x)


Note that erf(x) + erfc(x) = 1


Example:

erf(0.60):  0.6038560908

erfc(0.60):  0.3961439092



Law of Cosines


a^2 = b^2 + c^2 - 2*b*c*cos(α)


Finding the Angle α:  cosang(a,b,c)

Finding the Side a:  cosside(b,c,α)


Example:

(Degrees Mode)

a = 20.1, b = 18.5, c = 22.3:  cosang(20.1,18.5,22.3):  58.13961834°  (approx)

b = 24.2, c = 18.9, α = 58°:  cosside(24.2,18.9,58):  21.4032954 (approx)



Fresnel Integrals


Fresnel Cosine Integral:  frescos(u)

C(u) = ∫( cos(π * x^2 ÷ 2) dx, 0, u)


Fresnel Sine Integral:  fressin(u)

S(u) = ∫( sin(π * x^2 ÷ 2) dx, 0, u)


Example:

frescos(1.5):  0.445261176

fressin(1.5):  0.6975049601



Bessel Integral of the First Kind:  bessel(n,x)


J_n(x) = 1 / π * ∫( cos(n * t - x * sin t) dt, 0, π)


Example:

bessel(0,1.5):  0.5118276716

bessel(2,1.2):  0.1593490183



Elliptic Integral of the First Kind:  ellip(x)


K(x) = ∫( 1/ √(1 - x^2 * sin^2 t) dt, 0, π/2)


Example:

ellip(-0.6):  1.750753803

ellip(0.4):  1.639999866



Sine Integral:  Si(x)


Si(x) = ∫( sin t / t dt, 0, x)


Example:

Si(1.8):  1.50581678

Si(6):  1.424687551



Beta Function:  beta(a,b)


β(a, b) = (Γ(a) * Γ(b)) ÷ Γ(a+b)


Example:

beta(2,3): 1/12

beta(1.9,4.6):  0.04470413922 (approx)



Relativity Factor:  relat(v)


factor = √(1 - v^2/c^2)

c = 299792458 m/s

v = velocity


Example:

relat(201E6):  0.7419422153  (approx)



Schwarzschild Radius:  schwarz(m)


r = (2 * G * m)/c^2

G = 6.674E-11  m^3/(kg s^2)

c = 299792458 m/s

m = mass the black hole, kg

r = Schwarzschild Radius, m  (event horizon)


Example:

schwarz(7.89E30):  11717.95418



Distance of a Drop:  dropdist(v0,t)


v0:  initial velocity, m/s

t: time, s

Calculated:  distance, m


Example:

dropdist(15,5):  197.583125



Cycle of a Simple Pendulum:  pendu(l)


l:  length of a string, m

Calulated:  time of the pendulum swing, s


Example:  

pendu(5.5):  4.705446883



Impedance in LRC Series Circuit:  lrcser(R,f,L,C)


R:  resistance, Ω

f:  frequency, Hz

L:  inductance, H

C:  capacity, F


Example:

lrcser(4,80,0.1,50E-6):  11.21437564


Impedance in LRC Parallel Circuit:  lrcpar(R,f,L,C)


R:  resistance, Ω

f:  frequency, Hz

L:  inductance, H

C:  capacity, F


Example:

lrcpar(4,80,0.1,50E-6):  3.999122191



Source for:

Distance of a Drop

Cycle of a Simple Pendulum

Impedance in LRC Series Circuit

Impedance in LRC Parallel Circuit


Scientific Calculator 128 fx-1000F/fx-5000F Owner's Manual.   Casio.  Tokyo, Japan. 



Download the file here:  https://drive.google.com/file/d/1M54HlJ9dP95VBEmGzkUozGzJxKGpiHMh/view?usp=share_link



Eddie 



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