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Viète. de Moivre. Euler. Fourier. v. t. e. 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.
Pythagorean trigonometric identity. The Pythagorean trigonometric identity, also called simply the Pythagorean identity, is an identity expressing the Pythagorean theorem in terms of trigonometric functions. Along with the sum-of-angles formulae, it is one of the basic relations between the sine and cosine functions. The identity is.
The trigonometric function are periodic functions, and their primitive period is 2π for the sine and the cosine, and π for the tangent, which is increasing in each open interval (π/2 + kπ, π/2 + (k + 1)π). At each end point of these intervals, the tangent function has a vertical asymptote .
A right triangle with sides relative to an angle at the point. Inverse trigonometric functions are useful when trying to determine the remaining two angles of a right triangle when the lengths of the sides of the triangle are known. Recalling the right-triangle definitions of sine and cosine, it follows that.
The integral of the secant function was historically one of the first integrals of its type ever evaluated, before most of the development of integral calculus. It is important because it is the vertical coordinate of the Mercator projection, used for marine navigation with constant compass bearing .
Article One of the Constitution of the United States establishes the legislative branch of the federal government, the United States Congress. Under Article One, Congress is a bicameral legislature consisting of the House of Representatives and the Senate. [1] : 73 Article One grants Congress various enumerated powers and the ability to pass ...
In mathematics, the floor function (or greatest integer function) is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor (x). Similarly, the ceiling function maps x to the smallest integer greater than or equal to x, denoted ⌈x⌉ or ceil (x).
The Fourteenth Amendment (Amendment XIV) to the United States Constitution was adopted on July 9, 1868, as one of the Reconstruction Amendments.Usually considered one of the most consequential amendments, it addresses citizenship rights and equal protection under the law and was proposed in response to issues related to formerly enslaved Americans following the American Civil War.