Blumenthal, Leonard M. Formerly, Department of Mathematics, University of Missouri, Columbia, Missouri.
Last reviewed:June 2020
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The trigonometric tangent of the angle α that a line makes with the x axis as in Fig. 1. In Fig. 2 the slope of a plane curve C at a point P of C is the slope of the line that is tangent to C at P. If y = f(x) is an equation in rectangular coordinates of curve C, the slope of C at P(x0, y0) is the value of the derivative dy/dx = f′(x) at P, denoted by f′(x0), and hence an equation of the nonvertical tangent to C at P is y − y0 = f′(x0)(x − x0). See also: Analytic geometry; Calculus
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