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In the table below, the label "Undefined" represents a ratio : If the codomain of the trigonometric functions is taken to be the real numbers these entries are undefined , whereas if the codomain is taken to be the projectively extended real numbers , these entries take the value ∞ {\displaystyle \infty } (see division by zero ).
Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their corresponding side lengths are proportional.. In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) [1] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
(Also written as csc.) cosech – hyperbolic cosecant function. (Also written as csch.) cosh – hyperbolic cosine function. cosiv – coversine function. (Also written as cover, covers, cvs.) cot – cotangent function. (Also written as ctg.) coth – hyperbolic cotangent function. cov – covariance of a pair of random variables. cover ...
This operation is undefined in arithmetic, and therefore deductions based on division by zero can be contradictory. If we assume that a non-zero answer n {\displaystyle n} exists when some non-zero number k {\displaystyle k} is divided by zero, then that would imply that k = n × 0 {\displaystyle k=n\times 0} .
The oldest and most elementary definitions are based on the geometry of right triangles and the ratio between their sides. The proofs given in this article use these definitions, and thus apply to non-negative angles not greater than a right angle. For greater and negative angles, see Trigonometric functions.
Zero to the power of zero, denoted as 0 0, is a mathematical expression that can take different values depending on the context. In certain areas of mathematics, such as combinatorics and algebra, 0 0 is conventionally defined as 1 because this assignment simplifies many formulas and ensures consistency in operations involving exponents.
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 the ratio of the length of the adjacent leg to that ...
The points labelled 1, Sec(θ), Csc(θ) represent the length of the line segment from the origin to that point. Sin(θ), Tan(θ), and 1 are the heights to the line starting from the x-axis, while Cos(θ), 1, and Cot(θ) are lengths along the x-axis starting from the origin.