List of trigonometric identitiesIn 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. They are distinct from triangle identities, which are identities potentially involving angles but also involving side lengths or other lengths of a triangle. These identities are useful whenever expressions involving trigonometric functions need to be simplified.
DVDThe DVD (common abbreviation for Digital Video Disc or Digital Versatile Disc) is a digital optical disc data storage format. It was invented and developed in 1995 and first released on November 1, 1996, in Japan. The medium can store any kind of digital data and has been widely used for video programs (watched using DVD players) or formerly for storing software and other computer files as well. DVDs offer significantly higher storage capacity than compact discs (CD) while having the same dimensions.
PortugalPortugal (puɾtuˈɣal), officially the Portuguese Republic (República Portuguesa ʁɛˈpuβlikɐ puɾtuˈɣezɐ), is a country located on the Iberian Peninsula, in Southwestern Europe, and whose territory also includes the macaronesian archipelagos of the Azores, Madeira, and the Savage Islands. It features the westernmost point in continental Europe, and its Iberian portion is bordered to the west and south by the Atlantic Ocean and to the north and east by Spain, the sole country to have a land border with Portugal.
Power seriesIn mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the nth term and c is a constant. Power series are useful in mathematical analysis, where they arise as Taylor series of infinitely differentiable functions. In fact, Borel's theorem implies that every power series is the Taylor series of some smooth function. In many situations, c (the center of the series) is equal to zero, for instance when considering a Maclaurin series.
American Civil WarThe American Civil War (April 12, 1861 – May 26, 1865; also known by other names) was a civil war in the United States. It was fought between the Union ("the North") and the Confederacy ("the South"), the latter formed by states that had seceded. The central cause of the war was the dispute over whether slavery would be permitted to expand into the western territories, leading to more slave states, or be prevented from doing so, which many believed would place slavery on a course of ultimate extinction.
Harry PotterHarry Potter is a series of seven fantasy novels written by British author J. K. Rowling. The novels chronicle the lives of a young wizard, Harry Potter, and his friends Hermione Granger and Ron Weasley, all of whom are students at Hogwarts School of Witchcraft and Wizardry. The main story arc concerns Harry's conflict with Lord Voldemort, a dark wizard who intends to become immortal, overthrow the wizard governing body known as the Ministry of Magic and subjugate all wizards and Muggles (non-magical people).
Geometric seriesIn mathematics, a geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms. For example, the series is geometric, because each successive term can be obtained by multiplying the previous term by . In general, a geometric series is written as , where is the coefficient of each term and is the common ratio between adjacent terms.
Limit (mathematics)In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value. Limits are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals. The concept of a limit of a sequence is further generalized to the concept of a limit of a topological net, and is closely related to and direct limit in . In formulas, a limit of a function is usually written as (although a few authors use "Lt" instead of "lim") and is read as "the limit of f of x as x approaches c equals L".
Function (mathematics)In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a function of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity).
Rate-determining stepIn chemical kinetics, the overall rate of a reaction is often approximately determined by the slowest step, known as the rate-determining step (RDS or RD-step or r/d step) or rate-limiting step. For a given reaction mechanism, the prediction of the corresponding rate equation (for comparison with the experimental rate law) is often simplified by using this approximation of the rate-determining step. In principle, the time evolution of the reactant and product concentrations can be determined from the set of simultaneous rate equations for the individual steps of the mechanism, one for each step.
Enhanced Data rates for GSM EvolutionEnhanced Data rates for GSM Evolution (EDGE), also known as Enhanced GPRS (EGPRS), IMT Single Carrier (IMT-SC), or Enhanced Data rates for Global Evolution, is a digital mobile phone technology that allows improved data transmission rates as a backward-compatible extension of GSM. EDGE is considered a pre-3G radio technology and is part of ITU's 3G definition. EDGE was deployed on GSM networks beginning in 2003 – initially by Cingular (now AT&T) in the United States. EDGE is standardized also by 3GPP as part of the GSM family.
Convergence testsIn mathematics, convergence tests are methods of testing for the convergence, conditional convergence, absolute convergence, interval of convergence or divergence of an infinite series . If the limit of the summand is undefined or nonzero, that is , then the series must diverge. In this sense, the partial sums are Cauchy only if this limit exists and is equal to zero. The test is inconclusive if the limit of the summand is zero. This is also known as the nth-term test, test for divergence, or the divergence test.
