アメリカ緬甸 .網 MathematicalCalculations



s	(sine,	e.g. sine degree angle is equal to (opposite/hypotenuse)	6sComputer
S	SINE) =
o	(opposite,
O	OPPOSITE)
h	(hypotenuse,
H	HYPOTENUSE)

c	(cosine,	e.g. cosine degree angle is equal to (adjacent/hypotenuse)
C	COSINE) =
a	(adjacent,
A	ADJACENT)		3cComputer
h	(hypotenuse,
H	HYPOTENUSE)

t	(tangent,	e.g. tangent degree angle is equal to (opposite/adjacent)
T	TANGENT) =
o	(opposite,
O	OPPOSITE)
a	(adjacent,
A	ADJACENT)		9tComputer

(

kyokusen Curve,

Curve,

Curve), also see: c Character Extension1 (e.g. Curve);

curve; l Character (e.g. line); Mathematical Calculations (e.g.

Integral); (

Water Clock: aroma, fragrance, odor, perfume, redolence, savor, smell);

Name	Mathematical Calculations	Remark
cos^-1 ((SQRT3) / 2)	i.e. arc cosine (??) degree	... for each pair of moon waves;
Sine x	= (O p p / H y p)	doko WHERE 0 < x < π ;
(a^m)^n = a^mn		Power M (Multiplex) Power N
a^mn = (a^m)^n		Power M (Multiplex) Power N
log a^m = m log a		Power to a Log
log (a by b)		Minus
log a by log b		Base
log (Base c) a b		Plus
log (Base a) a		variable As Base
a log (Base a) b		Distance to b (Walls)
a^(log (Base a) b) = b		a trick like 9^2x = 9x Dot Product 9x
a^(log (Base a) b) = b		e.g. 10 (9 · 4) = 36 (10)

e.g. March 14, a.k.a. Pi Day (22/7 is 3.14, ((proportion, ratio,

Radical102) of (

kyori Distance,

kyori Distance)) around the circle to the distance across it) ... ; Also see: Mathematics; Mathematical Calculations; p Character;

(

log,

log) e.g. in Mathematical Calculations, log _{base can be any (Decimal, Fraction, Number)}, however (

, log 1 = 0, log _{(Decimal, Fraction, Number)} 1 = 0 ), i.e. very useful for Numerical values in numerology (log 1 is

Zero), e.g. Numerlogical0 ... , And Then, "

NOT log _{(Decimal,
Fraction, Number)} 1" (mean, prompt) numerological (Val. , Ref. ) so numerological dimensional (e.g. sizes of "ro" (

)), (numerological logical (e.g.

LoShu magic square,

Sudoku (

9)), also see: Network Topology), numerological structural (e.g. (magic, plot, stratagem, trap, trick,

Radical298), (measure, plan, plot, scheme,

Radical731), Scalar-Field (s), (

Table,

Table)), ... ; Remark: log a.k.a. logarithm; (

log,

log);

WHEN dealing with (

exponent,

exponent), (

exponent,

exponent), 1st to think of (Allow

OR (NOT Allow)); if Allow, find

WHICH (((

), (

)) rule, Rule, RULE, rules, ... ) to apply, e.g.

don't confuse with (?^2 (square ones, ?^3 (cube ones));
don't confuse with Mathematical Operators, N - A R Y SUMMATION (" ∑ ") ;

if Basic Latin, LATIN SMALL LETTER E ("e") ;
if Pre School English Typing .exe, ASCII ("101") ;
if Symbol, "e" in English language;
if Symbol, ESTIMATED SYMBOL (℮) ;
if Superscripts and Subscripts, ("ₑ") ;

Negative exponent indicates NOT multiplication;
Negative exponent means division (Method, Procedure, Technique);

regarding Mathematical Calculations, Log (at both sides) for solving exponents, if possible (Remark: sometime, impossible);
regarding Mathematical Calculations, can switch exponents, e.g.

, i.e. (2^x)^3 = (2^3)^x ;

regarding Mathematical Calculations, can switch exponents, e.g. (2^y)^3 = (2^3)^y ;

regarding Mathematical Calculations, can switch exponents, e.g. (2^z)^3 = (2^3)^z ;

WORMHOLE can connect 2 diff regions at the same Time ... (Reference Books, also read: Prof. Michio Kaku's PHYSICS books) ; can switch exponents, so Teleportation may begin i.e. (

cosmos,

space,

universe) ... ;

(

Zero,

One), related to exponents would be: "exponent 0" means 1, on the other hand, "exponent 1" means Number itself;

e.g. 2^9 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 ; e.g. 3^8 = 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 ;
e.g. 2^8 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 ; e.g. 3^7 = 3 * 3 * 3 * 3 * 3 * 3 * 3 ;
e.g. 2^7 = 2 * 2 * 2 * 2 * 2 * 2 * 2 ; e.g. 3^6 = 3 * 3 * 3 * 3 * 3 * 3 ;
e.g. 2^6 = 2 * 2 * 2 * 2 * 2 * 2 ; e.g. 3^5 = 3 * 3 * 3 * 3 * 3 ;
e.g. 2^5 = 2 * 2 * 2 * 2 * 2 ; e.g. 3^4 = 3 * 3 * 3 * 3 ;
e.g. 2^4 = 2 * 2 * 2 * 2 ; e.g. 3^3 = 3 * 3 * 3 ;
e.g. 2^3 = 2 * 2 * 2 ; e.g. 3^2 = 3 * 3 ;
e.g. 2^2 = 2 * 2 ; e.g. 3^1 = 3 ;
e.g. 2^1 = 2 ; e.g. 3^0 = 1 ;
e.g. 2^0 = 1 ;

(

exponent,

exponent), (

exponent,

exponent), also see: e Character; 5eComputer; Mathematical Calculations;

IFF Command (

line,

line)

Parameter,

And Then, type (e.g. C:\IT\ExecutableApplication\PreSchoolEnglishTyping.exe

)

And Then, type "!,"

And Then, realize & understand THAT ASCII numerical value of the key is 33,

WHICH has been used for (cheerful, grateful, wonderful, ... ) sign & symbol in English language, if compare to (factorial, Factorial, FACTORIAL) in Mathematics (Mathematical Calculations) ... e.g.

9! (mean (s), prompt (s), represent (s)) 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1;
8! (mean (s), prompt (s), represent (s)) 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1;
7! (mean (s), prompt (s), represent (s)) 7 * 6 * 5 * 4 * 3 * 2 * 1;
6! (mean (s), prompt (s), represent (s)) 6 * 5 * 4 * 3 * 2 * 1;
5! (mean (s), prompt (s), represent (s)) 5 * 4 * 3 * 2 * 1;
4! (mean (s), prompt (s), represent (s)) 4 * 3 * 2 * 1;
3! (mean (s), prompt (s), represent (s)) 3 * 2 * 1;
2! (mean (s), prompt (s), represent (s)) 2 * 1;
1! (mean (s), prompt (s), represent (s)) 1 * 1;
Remark: numerological linear calculations may begin ... ; numerological matrix (in common, (3 columns, 3 rows) calculations may begin ... ;

Binomial Coefficient e.g. (⁵₃) doko

WHERE

5 (choose, pick, select)

3, other wordings would be:

n (choose, pick, select)

k, calculated by fraction, e.g. take n 1st, And Then, apply formula

Binomial Coefficient (ⁿ_k) is equal to n! by (k! . (n-k)!), a.k.a. (ⁿ_k) = n! / (k! . (n-k)!) ... ;

in Computer Science . Browser, think of incoming Textbox (Val. , Ref. ) As FE (Front End), in this case, area of ". (n-k)!" ;

IFF Idea Processor (Buddha's Abhidharma based for humanoid nama) so

k should be 5 then;

IFF 1&1 design model, 2! with 1! would be very useful, regarding (factorial, Factorial, FACTORIAL) ... ;

WHEN, doko

WHERE, kuru kuru

WHILE calculating a

Curve,

Integral is ((calculation based on something (heard, read)

Radical951), deployed, implemented, used, utilized) with Limit (e.g. from minus to plus, from zero to infinity, from zero to one (a.k.a. decimal)) WHEN, WHERE, WHILE calculating a curve, based on a (

line,

line) line e.g. (a line on

x), ( a line on

y), ( a line on

z) ... regarding (SOH, CAH, TOA), Complexity Region (s) exist (if the line is a chord, if the line is a radius (i.e. related to

radian), if the line is a tangent), ... ,

And Then, don't forget R&D yourself by (Applying, Using) Circle Rules a.k.a. Circular Geometric Theorem ...

And Then, if from zero to one "decimal numbers" belong to (SQRT3, SQRT2),

And Then, floating points may begin ... so ((

Integral Upper Ref (TOP HALF INTEGRAL ("⌠"))), (

Integral Lower Ref (BOTTOM HALF INTEGRAL ("⌡")))) in Mathematical Calculations may (become, initialize)

aesthetics in

philosophy ... ;

(

INV,

INV), inverse function, a function THAT 's reversing another function;

e.g. (

DEG . cos) 's INV is cos^-1;
e.g. (

DEG . e) 's INV is (

R A D . e);
e.g. (

DEG . ln) 's INV is e^x;
e.g. (

DEG . log) 's INV is 10^x;
e.g. (

DEG . sin) 's INV is sin^-1;
e.g. (

DEG . tan) 's INV is tan^-1;
e.g. (

DEG . !) 's INV is (

R A D . !);
e.g. (

DEG . π) 's INV is (

R A D . π);
e.g. (

DEG . ^) 's INV is (

R A D . ^);
e.g. (

DEG . "(") 's INV is (

R A D . "(");
e.g. (

DEG . ")") 's INV is (

R A D . ")");
e.g. (

DEG . √) 's INV is x^2;

INV is INVERSE, i.e. math usage ... ; Also see: Mathematics;
INV is INVOICE, i.e. business usage ... ; Also see: Biz;

I wrote: I've created a picture i.e.

INVERSE, and I've a quiz: regarding (our earth, our moon), if I'm on the moon, HOW would the "INVERSE" would be?

well trained kids! replied: very easy quiz; since (area, environment) has lots of (Silver), Blue and Green are reversing each other sir;

I wrote: yes. so desu nal ... ; don't forget THAT (Yellow) and (Red) are also reversing ... ;


cos^-1	(		x	)
	OR	arccos	(		X	)

cos^-1	(		y	)
	OR	arccos	(		Y	)

cos^-1	(		z	)
	OR	arccos	(		Z	)

cos^-1	(		x	)
	NOT	(	1	/	cos (x)	)

cos^-1	(		y	)
	NOT	(	1	/	cos (y)	)

cos^-1	(		z	)
	NOT	(	1	/	cos (z)	)

if (

derivative,

derivative) derivatives, (arccos x) d/dx = - 1 / √(1-x^2) doko

WHERE x is (-1<x<1);

if Range, a.k.a. Principal Value (Val.), e.g. [0, π] radian

OR [0, 180] degree, so,

output can be (indicated, limited, restricted) by range;

if Replication function, ID should obey (

, arcsine (x) + arccos (x) = π divided by 2);

((

) i.e. Ln (1) = 0); in Mathematical Calculations, (Ln (1) a.k.a. Logarithm (1)) has been excluded, e.g. Keyword (nil, NULL) in Computer Science are neither Negative nor Positive (Also see: 8lComputer); other wordings would be

NOT calculating Ln (1), however i.e. very useful in numerological, e.g. Numerological0, because non-zero (factors, floating points (SQRT3), floating points (SQRT2), numerical numbers, numerological mapped numbers) can be PCS based computing (since 2025) in addition to ZCS based computing, ... ; Reminder: because of PCS based computing, in the near future,

ware ware We'll have (aroma, fragrance, odor, perfume, redolence, savor, smell), kuru kuru

WHILE watching movie ... ; Remark:

sayana (Stage, State, Status) is very important "New Usage," regarding neither Negative nor Positive ;

you may R&D yourself, e.g. kuru kuru WHILE calculating derivatives, if integer whole numbers prompt, then replace with zero ... ;
you may R&D yourself, e.g. kuru kuru WHILE calculating Logarithm, if Ln (1) prompt, then replace with zero ... ;
you may R&D yourself, e.g. kuru kuru WHILE calculating x, exponents of derivatives x should be excluded (nil, NULL);
you may R&D yourself, e.g. kuru kuru WHILE calculating y, exponents of derivatives y should be excluded (nil, NULL);
you may R&D yourself, e.g. kuru kuru WHILE calculating z, exponents of derivatives z should be excluded (nil, NULL);

if DAL, don't forget THAT

is equal to Ln

, also see: Schematic Symbols (

Y = Ln X), a.k.a.

e constant, ... ;

(

ODE,

ODE), Ordinary Differential Equations (ODE) i.e.

NOT partial differential equations, e.g.

WHAT is ODE? Answer would be among

derivatives,

form (s), (((measure, plan, plot, scheme,

Radical731), (magic, plot, stratagem, trap, trick,

Radical298)) plot (s)), ((

Table,

Table) table (s)), Scalar-Field (s), e.g.

small amount of (

x) would be 'dx' ... ,
small amount of (

y) would be 'dy' ... ,
small amount of (

z) would be 'dz' ... ,

regarding Basic (x, X), if (

interval, Real-time, timeslot) are needed in Mathematics, e.g. ( x +

3 = 2^2 ) can be represented as 3x/dt +

3 = 2^2, so instead of "x," its derivatives (in this case: dx/dt) doko

WHERE t (-time, Time) is, so ODE can be realized & understood; another example in (2 * 6) momentum (our earth) would be Newton's (F = ma) doko

WHERE acceleration "a" can be 2nd derivatives (e.g. a = (dv (Velocity)) / dt (Time)) = 2nd derivatives on "x" (d^2 x / d t^2 (-time)) WHERE "m" is a Number

AND 2nd derivatives of its (

position,

position) "a", also see:

2; Mathematical Calculations; 6oComputer; by the way, in Computer Science, if you know

five e.g. (Left's 5, Right's 5),

And Then, you should be global military generals (if nothing to do with money),

OR you should be billionaires of

US Dollar rich (if something to do with money (e.g. donations, gifts, ... )), and don't forget THAT KNOWLEDGE IS POWER, starting from e.g. the most challenge in 21st century & beyond would be Anti-Earthquake design model, Gene Therapy System (fully

Recovery to WHOM) by Nanobot Programming, Natural Water Elevator (kadosei Mobility, PCS based computing in addition to ZCS based computing (since 2025), ZCS based computing), ... ;

kuru kuru WHILE dealing with squared x, (e.g. x^2),
kuru kuru WHILE dealing with squared y, (e.g. y^2),
kuru kuru WHILE dealing with squared z, (e.g. z^2),

quadratic (General Form, general term) e.g. (ax^2 + bx + c = 0) a.k.a. (ax² + bx + c = 0) ... ; Remark: kuru kuru

WHILE factoring, in common,

4ac has been used in Quadratic Formula ... ; Reminder: apply to (x^2, y^2, z^2) squared ones only

AND (

NOT For (x^3, y^3, z^3)) ... ;

Remark: in Computer Science (

cosmos,

space,

universe), don't confuse between (

15 degree by SQRT2 longitudes) and ((SQRT15)/2), and recommended formulary for Mathematical Calculations, e.g.

, i.e. (x - a)^2 + ( y - b)^2 = r^2 As Radius; Also see:

radian;

, i.e. a^2 + 2ab + b^2 = (a + b)^2 As Pythagorean;

, i.e. Distance (d) = √((x₁ - x₂)^2 + (y₁ - y₂)^2) As Hypotenuse;

, i.e. (f (x, y) = ((x^2) + (y^2)) = 13 WHEN ((x = 3) and (y = 2))), a.k.a. f (x, y) = ((x^2) + (y^2)) Output

WHEN ((

x=3)

AND (

y=2)), a.k.a. FUNCTION OF (

Y) is equal to 'X SQUARE' plus 'Y SQUARE' ; Remark: doko

WHERE 500.98+ would be:

remote ((0.5), (1/2), (1:2)), a.k.a. Half Way (Method, Procedure, Technique) in Network Topology ... ; kuru kuru

WHILE dealing with many (

derivative,

derivative) derivatives e.g. multi-systems (

Time) should be 1st priority, e.g.

nitotte For DOMAIN [-1, +1], Laplace Transform (Method, Procedure, Technique) should be calculated, deployed, implemented, measured, used, utilized, ... ; Also see:

2; Mathematical Calculations;

radian; since 1980s, multi-systems inventor Toshiba has been very very very genius ... ;

Quotient Rule, e.g. cos^-1 (SQRT3/2)

nitotte For

kaku Each pair of moon waves in degree,

And Then, Quotient Rule for fraction, e.g.

Quotient Rule for fraction ƒ (z) = u ÷ v , And Then, it derivative ƒ ' (z) = ( u ' . v - u . v ' ) ÷ v^2; Also see:

2; Anti-Earthquake; d Computer (derivative); Mathematical Calculations; area between curves, 1st. intersecting points (e.g. 1 chord of 2 circles); 2nd. using Absolute Value (a.k.a. Val. ) Bar i.e. using "| |" e.g.

3rd. solve integral; 4th. anti-derivative; 5th. years ahead, in our earth, NOT EXIST (Earthquake) prompt means the Shakya King will GRANT DEED (

Me,

Me) 1 whole human beings livable moon among many human beings livable moons in our universes ... ;

well trained kids!! replied: HOW can we calculate to solve integral sir?
I wrote: OH!! OH!! You need to realize & understand 180 degree to the defined USB, good example would be:

WHEN very very fast trains are traveling at a curve, to maintain (on tracks + its speed) means dubbing DEE spot at 180 degree to the defined USB, so results of (

Elevating,

Landing) for each side (of the very very fast trains) can be calculated by Processor , so called "Side-by-Side Processor" ... ; Remark: this info is worth more than trillions of US Dollar; till 2026, I still cannot dub my 2024 Toyota Land cruiser 1958 Edition's front lights ... ;

2008 Fuzzy mathematical calculation, (also see: http://documents . wolf ram .com / applications / fuzzy logic / Manual /10 .html), so that addition, subtraction, multiplication, image, max function, min function, ... can be further studied in fuzzy approach ... ;

2007 ADC's distortion causes its sample rate becomes (sample rate / 2), and bandwidth signal [i.e. S N R 50dB at 12bit per 1G sample per second] prompts, and then processing gain can be calculated as:
processing gain = -10(log(bandwidth_signal/(sample rate/2))).
If jitter, for the given system, S N R to jitter calculated as:
S N R is approximately -20(log₁₀((2π_cycle f_{frequency _input}) (t_jitter))) ;

2007 I P M motor's Torque: Depending on types of motor, calculation may vary; In I P M motor [e.g. air con compressor motor], when calculating magnet _torque and reluctance _torque, 2 * rotor angle in sine is used as:
torque T = P_n ((Φ * ampere I * (cosine (β))) + (1/2(inductance L_q - inductance L_d) * (square (ampere I)) ) * sine(2 * β)); AC input into rectifier, and then normal power supply P_n can be measured. The given F O C is sensor-less. Velocity control can be further studied. IFF 2 phase circuit, while current I is looping, flux can be estimated, because the circuit's back E M F are in cosine and sine as: volt V₁ = (resistance R_s * current I₁) + (inductance L_s * (dI₁/ d t vary I1 at time t)) + (d / d t at time t(-Ψ_r * cosine (θ_r))); V₂ = (resistance R_s * current I₂) + (inductance L_s * (dI₂/d t vary I2 at time t)) + (d / d t at time t(-Ψ_r * sine (θ_r))); WHERE rotor's flux angle in cosine and sine are as: Ψ_r * cosine (θ_r) = integration ∫ integral in distance as ∫((resistance R_s * current I₁) - V₁) + (inductance L_s * I₁); Ψ_r * sine (θ_r) = ∫((resistance R_s * current I₂) - V₂) + (inductance L_s * I₂);