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  1. 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...

  2. en.wikipedia.org › wiki › X̂X̂ - Wikipedia

    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.

  3. 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.

  4. 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.

  5. Euler's formula is ubiquitous in mathematics, physics, chemistry, and engineering. The physicist Richard Feynman called the equation "our jewel" and "the most remarkable formula in mathematics". [2] When x = π, Euler's formula may be rewritten as eiπ + 1 = 0 or eiπ = -1, which is known as Euler's identity .

  6. 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 .

  7. 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] .