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[zh-TW]: create Math.acosh() (#25121)
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Co-authored-by: A1lo <[email protected]>
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Dr-XYZ and yin1999 authored Dec 19, 2024
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---
title: Math.acosh()
slug: Web/JavaScript/Reference/Global_Objects/Math/acosh
l10n:
sourceCommit: 761b9047d78876cbd153be811efb1aa77b419877
---

{{JSRef}}

**`Math.acosh()`** 靜態方法回傳數字的反雙曲餘弦值。也就是說,

<math display="block">
<semantics><mtable columnalign="right left right left right left right left right left" columnspacing="0em" displaystyle="true"><mtr><mtd><mo>∀</mo><mi>x</mi><mo>≥</mo><mn>1</mn><mo>,</mo><mspace width="0.2777777777777778em"></mspace><mrow><mo lspace="0em" rspace="0.16666666666666666em">𝙼𝚊𝚝𝚑.𝚊𝚌𝚘𝚜𝚑</mo><mo stretchy="false">(</mo><mi>𝚡</mi><mo stretchy="false">)</mo></mrow></mtd><mtd><mo>=</mo><mo lspace="0em" rspace="0.16666666666666666em">arcosh</mo><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mtext>the unique&nbsp;</mtext><mi>y</mi><mo>≥</mo><mn>0</mn><mtext>&nbsp;such that&nbsp;</mtext><mo lspace="0em" rspace="0em">cosh</mo><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mo>=</mo><mi>x</mi></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo><mo lspace="0em" rspace="0em">ln</mo><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><msqrt><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>1</mn></mrow></msqrt></mrow><mo>)</mo></mrow></mtd></mtr></mtable><annotation encoding="TeX">\begin{aligned}\forall x \geq 1,\;\mathtt{\operatorname{Math.acosh}(x)} &= \operatorname{arcosh}(x) = \text{the unique } y \geq 0 \text{ such that } \cosh(y) = x\\&= \ln\left(x + \sqrt{x^2 - 1}\right)\end{aligned}</annotation></semantics>
</math>

{{EmbedInteractiveExample("pages/js/math-acosh.html")}}

## 語法

```js-nolint
Math.acosh(x)
```

### 參數

- `x`
- : 一個大於或等於 1 的數字。

### 回傳值

`x` 的反雙曲餘弦值。如果 `x` 小於 1,則回傳 {{jsxref("NaN")}}。

## 描述

由於 `acosh()``Math` 的靜態方法,你必須使用 `Math.acosh()` 來呼叫它,而非呼叫你建立的 `Math` 物件的方法(`Math` 並非建構子)。

## 範例

### 使用 Math.acosh()

```js
Math.acosh(0); // NaN
Math.acosh(1); // 0
Math.acosh(2); // 1.3169578969248166
Math.acosh(Infinity); // Infinity
```

## 規範

{{Specifications}}

## 瀏覽器相容性

{{Compat}}

## 參見

- [`core-js``Math.acosh` 的 polyfill](https://github.com/zloirock/core-js#ecmascript-math)
- {{jsxref("Math.asinh()")}}
- {{jsxref("Math.atanh()")}}
- {{jsxref("Math.cosh()")}}
- {{jsxref("Math.sinh()")}}
- {{jsxref("Math.tanh()")}}

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