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The other four trigonometric functions (tan, cot, sec, csc) can be defined as quotients and reciprocals of sin and cos, except where zero occurs in the denominator. It can be proved, for real arguments, that these definitions coincide with elementary geometric definitions if the argument is regarded as an angle in radians. [ 5 ]
Ptolemy's theorem states that the sum of the products of the lengths of opposite sides is equal to the product of the lengths of the diagonals. When those side-lengths are expressed in terms of the sin and cos values shown in the figure above, this yields the angle sum trigonometric identity for sine: sin(α + β) = sin α cos β + cos α sin β.
In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is ...
Hyperbolic functions occur in the calculations of angles and distances in hyperbolic geometry. They also occur in the solutions of many linear differential equations (such as the equation defining a catenary), cubic equations, and Laplace's equation in Cartesian coordinates. Laplace's equations are important in many areas of physics, including ...
Desmos was founded by Eli Luberoff, a math and physics double major from Yale University, [3] and was launched as a startup at TechCrunch 's Disrupt New York conference in 2011. [4] As of September 2012, it had received around 1 million US dollars of funding from Kapor Capital, Learn Capital, Kindler Capital, Elm Street Ventures and Google ...
Axiom is a general-purpose computer algebra system. It has been in development since 1971 by IBM, and was originally named scratchpad. Richard Jenks originally headed it but over the years Barry Trager who then shaped the direction of the scratchpad project took over the project. It was eventually sold to the Numerical Algorithms Group (NAG ...