搜尋結果
The Australian dollar ( sign: $; code: AUD; also abbreviated A$ or sometimes AU$ to distinguish it from other dollar-denominated currencies; [2] [3] and also referred to as the dollar or Aussie dollar) is the official currency and legal tender of Australia, including all of its external territories, and three independent sovereign Pacific Island...
- 21.4880+0.0450 (+0.2098%)截至 2024年6月07日, 週五 上午 5:35 TST · (TWD)。(報價延遲20分鐘)。市場開市中。
- 昨收21.4430開盤21.4460委買價21.4880 x 不適用委賣價21.5880 x 不適用
- 今日價格區間21.4080 - 21.534052週價格區間18.9176 - 21.6522成交量不適用平均成交量不適用
- 市值不適用本益比 (最近12個月)不適用營運報告/法說會日期不適用除權除息日-
相關股票
X̂ is the Latin letter X with a circumflex. The letter is used in the modern orthography of the Aleut language [1] and in the current Alaska Native Language Center alphabet of the Haida language. [2] In both cases, it represents the sound [ χ] . In mathematics, x̂ often refers to the unit vector in the +X direction.
In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles.
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) [1] [2] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
- History
- Definitions of Complex Exponentiation
- Applications
- Other Special Cases
- See Also
- Further Reading
In 1714, the English mathematician Roger Cotes presented a geometrical argument that can be interpreted (after correcting a misplaced factor of − 1 {\displaystyle {\sqrt {-1}}} ) as: Around 1740 Leonhard Euler turned his attention to the exponential function and derived the equation named after him by comparing the series expansions of the exponent...
The exponential function ex for real values of x may be defined in a few different equivalent ways (see Characterizations of the exponential function). Several of these methods may be directly extended to give definitions of ez for complex values of z simply by substituting z in place of x and using the complex algebraic operations. In particular, ...
Topological interpretation
In the language of topology, Euler's formula states that the imaginary exponential function t ↦ e i t {\displaystyle t\mapsto e^{it}} is a (surjective) morphism of topological groups from the real line R {\displaystyle \mathbb {R} } to the unit circle S 1 {\displaystyle \mathbb {S} ^{1}} . In fact, this exhibits R {\displaystyle \mathbb {R} } as a covering space of S 1 {\displaystyle \mathbb {S} ^{1}} . Similarly, Euler's identity says that the kernel of this map is τ Z {\displaystyle \tau \m...
Other applications
In differential equations, the function eix is often used to simplify solutions, even if the final answer is a real function involving sine and cosine. The reason for this is that the exponential function is the eigenfunction of the operation of differentiation. In electrical engineering, signal processing, and similar fields, signals that vary periodically over time are often described as a combination of sinusoidal functions (see Fourier analysis), and these are more conveniently expressed...
The special casesthat evaluate to units illustrate rotation around the complex unit circle: The special case at x = τ (where τ = 2π, one turn) yields eiτ = 1 + 0. This is also argued to link five fundamental constants with three basic arithmetic operations, but, unlike Euler's identity, without rearranging the addendsfrom the general case:
Nahin, Paul J. (2006). Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills. Princeton University Press. ISBN 978-0-691-11822-2.Wilson, Robin (2018). Euler's Pioneering Equation: The Most Beautiful Theorem in Mathematics. Oxford: Oxford University Press. ISBN 978-0-19-879492-9. MR 3791469.In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here ), and is denoted by the symbol .
The New Taiwan dollar [I] ( code: TWD; symbol: NT$, also abbreviated as NT) is the official currency of the Republic of China. The New Taiwan dollar has been the currency of the island of Taiwan since 1949, when it replaced the old Taiwan dollar, at a rate of 40,000 old dollars per one new dollar. [1] .
