Lembaran Cheat Objek Matematik JavaScript

Objek Matematik dalam JavaScript menyediakan satu set sifat dan kaedah untuk melaksanakan tugasan matematik. Berikut ialah helaian tipu yang komprehensif untuk objek Matematik.

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Hartanah

Objek Matematik mempunyai set pemalar:

Property	Description	Value (Approx.)
Math.E	Euler's number	2.718
Math.LN2	Natural logarithm of 2	0.693
Math.LN10	Natural logarithm of 10	2.302
Math.LOG2E	Base 2 logarithm of Math.E	1.442
Math.LOG10E	Base 10 logarithm of Math.E	0.434
Math.PI	Ratio of a circle's circumference to its diameter	3.14159
Math.SQRT1_2	Square root of 1/2	0.707
Math.SQRT2	Square root of 2	1.414

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Kaedah

1. Kaedah Pembundaran

Method	Description	Example
Math.round(x)	Rounds to the nearest integer	Math.round(4.5) → 5
Math.floor(x)	Rounds down to the nearest integer	Math.floor(4.7) → 4
Math.ceil(x)	Rounds up to the nearest integer	Math.ceil(4.1) → 5
Math.trunc(x)	Removes the decimal part (truncates)	Math.trunc(4.9) → 4

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2. Penjanaan Nombor Rawak

Method	Description	Example
Math.random()	Generates a random number between 0 and 1 (exclusive)	Math.random() → 0.53
Custom Random Int Generator	Random integer between min and max	Math.floor(Math.random() * (max - min 1)) min

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3. Kaedah Aritmetik

Method	Description	Example
Math.abs(x)	Absolute value	Math.abs(-7) → 7
Math.pow(x, y)	Raises x to the power of y	Math.pow(2, 3) → 8
Math.sqrt(x)	Square root of x	Math.sqrt(16) → 4
Math.cbrt(x)	Cube root of x	Math.cbrt(27) → 3
Math.hypot(...values)	Square root of the sum of squares of arguments	Math.hypot(3, 4) → 5

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4. Kaedah Eksponen dan Logaritma

Method	Description	Example
Math.exp(x)	e^x	Math.exp(1) → 2.718
Math.log(x)	Natural logarithm (ln(x))	Math.log(10) → 2.302
Math.log2(x)	Base 2 logarithm of x	Math.log2(8) → 3
Math.log10(x)	Base 10 logarithm of x	Math.log10(100) → 2

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5. Kaedah Trigonometri

Method	Description	Example
Math.sin(x)	Sine of x (x in radians)	Math.sin(Math.PI / 2) → 1
Math.cos(x)	Cosine of x (x in radians)	Math.cos(0) → 1
Math.tan(x)	Tangent of x (x in radians)	Math.tan(Math.PI / 4) → 1
Math.asin(x)	Arcsine of x (returns radians)	Math.asin(1) → 1.57
Math.acos(x)	Arccosine of x	Math.acos(1) → 0
Math.atan(x)	Arctangent of x	Math.atan(1) → 0.785
Math.atan2(y, x)	Arctangent of y / x	Math.atan2(1, 1) → 0.785

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6. Min, Maks dan Pengapit

Method	Description	Example
Math.max(...values)	Returns the largest value	Math.max(5, 10, 15) → 15
Math.min(...values)	Returns the smallest value	Math.min(5, 10, 15) → 5
Custom Clamping	Restrict a value to a range	Math.min(Math.max(x, min), max)

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7. Kaedah Lain

Method	Description	Example
Math.sign(x)	Returns 1, -1, or 0 based on sign of x	Math.sign(-10) → -1
Math.fround(x)	Nearest 32-bit floating-point number	Math.fround(5.5) → 5.5
Math.clz32(x)	Counts leading zero bits in 32-bit binary	Math.clz32(1) → 31

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Contoh

Integer Rawak Antara 1 dan 100

const randomInt = Math.floor(Math.random() * 100) + 1;
console.log(randomInt);

Kira Luas Bulatan

const radius = 5;
const area = Math.PI * Math.pow(radius, 2);
console.log(area); // 78.54

Tukar Darjah kepada Radian

const degrees = 90;
const radians = degrees * (Math.PI / 180);
console.log(radians); // 1.57

Cari Nombor Terbesar dalam Tatasusunan

const nums = [5, 3, 9, 1];
console.log(Math.max(...nums)); // 9

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Kes Penggunaan Lanjutan untuk Objek Matematik

Objek Matematik mempunyai banyak aplikasi praktikal. Berikut ialah senarai senario biasa dan contoh untuk menggambarkan cara menggunakannya dengan berkesan.

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1. Rawak

Hasilkan Integer Rawak Dalam Julat

function getRandomInt(min, max) {
    return Math.floor(Math.random() * (max - min + 1)) + min;
}
console.log(getRandomInt(1, 10)); // Random number between 1 and 10

Kocok Tatasusunan

function shuffleArray(arr) {
    return arr.sort(() => Math.random() - 0.5);
}
console.log(shuffleArray([1, 2, 3, 4, 5])); // Shuffled array

Simulasikan Gulungan Dadu

function rollDice() {
    return Math.floor(Math.random() * 6) + 1; // Random number between 1 and 6
}
console.log(rollDice());

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2. Geometri dan Bentuk

Kira Luas Bulatan

const radius = 5;
const area = Math.PI * Math.pow(radius, 2);
console.log(area); // 78.54

Kira Hipotenus Segi Tiga

const a = 3, b = 4;
const hypotenuse = Math.hypot(a, b);
console.log(hypotenuse); // 5

Tukar Darjah kepada Radian

function degreesToRadians(degrees) {
    return degrees * (Math.PI / 180);
}
console.log(degreesToRadians(90)); // 1.57

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3. Kewangan dan Perniagaan

Formula Faedah Kompaun

function compoundInterest(principal, rate, time, n) {
    return principal * Math.pow((1 + rate / n), n * time);
}
console.log(compoundInterest(1000, 0.05, 10, 12)); // 47.01

Membundarkan Nilai Mata Wang

const amount = 19.56789;
const rounded = Math.round(amount * 100) / 100; // Round to 2 decimal places
console.log(rounded); // 19.57

Kira Diskaun

function calculateDiscount(price, discount) {
    return Math.floor(price * (1 - discount / 100));
}
console.log(calculateDiscount(200, 15)); // 0

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4. Permainan dan Animasi

Simulasikan Lambungan Syiling

function coinToss() {
    return Math.random() < 0.5 ? 'Heads' : 'Tails';
}
console.log(coinToss());

Fungsi Pelonggaran untuk Animasi Lancar

function easeOutQuad(t) {
    return t * (2 - t); // Simple easing function
}
console.log(easeOutQuad(0.5)); // 0.75

Koordinat Pemijahan Rawak dalam Grid 2D

function randomCoordinates(gridSize) {
    const x = Math.floor(Math.random() * gridSize);
    const y = Math.floor(Math.random() * gridSize);
    return { x, y };
}
console.log(randomCoordinates(10)); // e.g., {x: 7, y: 2}

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5. Analisis Data

Cari Maksimum dan Minimum dalam Tatasusunan

const scores = [85, 90, 78, 92, 88];
console.log(Math.max(...scores)); // 92
console.log(Math.min(...scores)); // 78

Normalkan Data

function normalize(value, min, max) {
    return (value - min) / (max - min);
}
console.log(normalize(75, 0, 100)); // 0.75

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6. Fizik dan Kejuruteraan

Kira Halaju Selepas Jatuh Bebas

const gravity = 9.8; // m/s^2
const time = 3; // seconds
const velocity = gravity * time;
console.log(velocity); // 29.4 m/s

Tempoh Bandul

function pendulumPeriod(length) {
    return 2 * Math.PI * Math.sqrt(length / 9.8);
}
console.log(pendulumPeriod(1)); // 2.006 seconds

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7. Manipulasi Nombor

Kapit Nombor Dalam Julat

function clamp(value, min, max) {
    return Math.min(Math.max(value, min), max);
}
console.log(clamp(15, 10, 20)); // 15
console.log(clamp(5, 10, 20));  // 10

Tukarkan Nombor Negatif kepada Positif

console.log(Math.abs(-42)); // 42

Cari Bahagian Integer Nombor

console.log(Math.trunc(4.9)); // 4
console.log(Math.trunc(-4.9)); // -4

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8. Penyelesaian Masalah

Semak sama ada Nombor ialah Kuasa 2

function isPowerOfTwo(n) {
    return Math.log2(n) % 1 === 0;
}
console.log(isPowerOfTwo(8)); // true
console.log(isPowerOfTwo(10)); // false

Hasilkan Nombor Fibonacci

function fibonacci(n) {
    const phi = (1 + Math.sqrt(5)) / 2;
    return Math.round((Math.pow(phi, n) - Math.pow(-phi, -n)) / Math.sqrt(5));
}
console.log(fibonacci(10)); // 55

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9. Pelbagai

Hasilkan Warna Rawak (RGB)

function getRandomColor() {
    const r = Math.floor(Math.random() * 256);
    const g = Math.floor(Math.random() * 256);
    const b = Math.floor(Math.random() * 256);
    return `rgb(${r}, ${g}, ${b})`;
}
console.log(getRandomColor()); // e.g., rgb(123, 45, 67)

Kira Umur dari Tarikh Lahir

function calculateAge(birthYear) {
    const currentYear = new Date().getFullYear();
    return currentYear - birthYear;
}
console.log(calculateAge(1990)); // e.g., 34

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