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The intuitive notion that a tangent line "touches" a curve can be made more explicit by considering the sequence of straight lines (secant lines) passing through two points, A and B, those that lie on the function curve. The tangent at A is the limit when point B approximates or tends to A. The existence and uniqueness of the tangent line ...
The trigonometric functions most widely used in modern mathematics are the sine, the cosine, and the tangent functions. Their reciprocals are respectively the cosecant, the secant, and the cotangent functions, which are less used.
In trigonometry, the law of tangents or tangent rule [1] is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides. In Figure 1, a , b , and c are the lengths of the three sides of the triangle, and α , β , and γ are the angles opposite those three respective sides.
Scientific calculators have buttons for calculating the main trigonometric functions (sin, cos, tan, and sometimes cis and their inverses). [51] Most allow a choice of angle measurement methods: degrees, radians, and sometimes gradians. Most computer programming languages provide function libraries that include the trigonometric functions. [52]
Similar right triangles illustrating the tangent and secant trigonometric functions Trigonometric functions and their reciprocals on the unit circle. The Pythagorean theorem applied to the blue triangle shows the identity 1 + cot 2 θ = csc 2 θ, and applied to the red triangle shows that 1 + tan 2 θ = sec 2 θ.
The sine and tangent small-angle approximations are used in relation to the double-slit experiment or a diffraction grating to develop simplified equations like the following, where y is the distance of a fringe from the center of maximum light intensity, m is the order of the fringe, D is the distance between the slits and projection screen ...
More generally, in geometry, two curves are said to be tangent when they intersect at a given point and have the same direction at that point; see for instance tangent circles; Bitangent, a line that is tangent to two different curves, or tangent twice to the same curve; The tangent function, one of the six basic trigonometric functions
In mathematics, a tangent vector is a vector that is tangent to a curve or surface at a given point. Tangent vectors are described in the differential geometry of curves in the context of curves in R n. More generally, tangent vectors are elements of a tangent space of a differentiable manifold. Tangent vectors can also be described in terms of ...