Csc Is Cosec, Oct 27, 2026 · The cosecant cscz is the function defined by cscz = 1/(sinz) (1) = (2i)/(e^(iz)-e^(-iz)), (2) where sinz is the sine and sinz!=0. For tan and sec, the denominator is the length from the origin to (1,0); and for cot and cosec it's from the origin to (0,1) (or perhaps from (cot (𝜃),0) to (cot (𝜃),1) if you want to see where 𝜃 is more clearly. 222; Gradshteyn and Ryzhik 2000, p. Euler (1748) and T. Cosecant is also abbreviated as cosec. 25 csc or cosec — trigonometric cosecant function 1. von Lauchen Rheticus (1596) and E. Reference. Also, see solved examples on how to calculate the cosecant of The cosecant function is the reciprocal of the sine function. You might like to read about Trigonometry first! The Trigonometric Identities are equations that are true for right triangles. 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. Secant, cosecant and cotangent are usually written as sec, cosec and cot, they are trigonometric functions. We know that sin x is equal to for all integral multiples of pi, that is, sin x = 0 implies that that x = nπ, where n is an integer. Gunter (around 1620). Trigonometry is a branch of mathematics that studies May 29, 2017 · The cosecant (csc ${\displaystyle \mathrm{csc}}$), secant (sec ${\displaystyle \mathrm{sec}}$) and cotangent (cot ${\displaystyle \mathrm{cot}}$) functions are 'convenience' functions, just the reciprocals of (that is 1 divided by) the sine, cosine and tangent. In a formula, it is abbreviated to just 'csc'. It is represented by the symbol csc or cosec. The Formula for Cosec x is Given as: The Art of Mathematics Help 6. Definition Cosecant of the angle is ratio of the hypotenuse to opposite leg. 1989, p. Half-Angle formulas, Product and Sum Formulas. For any angle θ where sin θ ≠ 0, the cosecant gives the ratio of the hypotenuse to Domain and Range of Cosec x As we discussed before, cosecant is the reciprocal of the sine function, that is, csc x = 1 / sin x, cosec x is defined for all real numbers except for values where sin x is equal to zero. Graph Cosecant is 2π periodic function defined everywhere on real axis, except its singular points πn, n = 0, ±1, ±2, — so function domain is (πn, π (n + 1)), n∈N. Khan Academy does not support this browser. It is abbreviated as csc x or cosec x, where x is the angle. The word Cosecant is one of the six trigonometric ratios which is also denoted as cosec or csc. csc (−θ) = - csc θ . The abbreviation of cotangent is cot. Math Dictionary cosecant (cosec or csc) A trigonometric function of an angle equal to the reciprocal of its sine, that is, cosecant x = 1 / sin x Cosecant, often abbreviated as cosec or cosech, is one of the trigonometric functions used in mathematics. xxix). 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. Cosecant is used extensively in geometry, trigonometry, and calculus to solve various mathematical problems. The formula for Cosec x In this section we define sine, cosine and tangent, as well as the reciproacla ratios, csc, sec and cot. 16 csc or cosec — trigonometric cosecant function Category. Csc sec cot are based on the other three trigonometric functions sin, cos, and tan, respectively. Cosecant What is the Cosecant? In trigonometry, the cosecant is a function that associates an angle α with the reciprocal of its sine. It is the inverse (reciprocal) ratio of the sine function and is the ratio of the Hypotenus and Opposite sides in a right-angle triangle. It was widely used by L. The following diagram shows the Reciprocal Trigonometric Functions. ) Reply reply stellarstella77 • Oct 1, 2026 · Calculate the secant, cosecant, and cotangent functions using the sides of a triangle. This implies when the sine approaches 0, then csc approaches infinity. Definition of the cosecant function, csc x, and its properties and graph are presented. When the length of the hypotenuse is divided by the length of the opposite side, it gives the Cosecant of an angle in a right triangle. The cosecant function is a trigonometric function and is the reciprocal of the sine function. The cosecant formula is given by the length of the hypotenuse divided by the length of the opposite side in a right triangle. Cosec x Formula If the length of the hypotenuse is divided by the length of the opposite side, it provides the Cosecant of an angle in a right triangle. In this article, we have covered, in brief, trigonometric ratios, the Cosecant Formula, related examples and Understand what cosecant is and the formula for calculating the cosecant of an angle. . Example: For sin and cos, the denominator is the radius of the unit circle. Of the six possible trigonometric functions, cosecant, cotangent, and secant, are rarely used. It was mentioned in the works of G. Csc Elementary Functions Csc [z] Introduction to the Cosecant Function Defining the cosecant function The cosecant function is an old mathematical function. The cosecant is implemented in the Wolfram Language as Csc[z]. Abstract. Olivier, Wait, and Jones (1881). Csc sec cot are the three trigonometric functions cosecant, secant, and cotangent respectively. This article is a part of Librow scientific formula calculator project. ) From the definition of the cotangent of angle A, cot A = length of side adjacent to angle A/ length of side opposite to angle A, and the Pythagorean theorem, one has the useful identity cot 2 A + 1 = csc 2 A. One of the trigonometric functions in trigonometry, it is represented as Cosec and occasionally abbreviated as csc. 2. Jul 23, 2025 · Cosecant is one of the six basic trigonometric ratios and its formula is cosecant (θ) = hypotenuse/opposite, it is also represented as, csc (θ). The reciprocal of the cosecant is the sine: 1/ csc A = sin A. [5] Cosecant is the reciprocal of the sine function, written as csc θ = 1/sin θ. May 28, 2021 · This section addresses the graphing of the cosecant and secant curves. To use Khan Academy you need to upgrade to another web browser. Since it is the reciprocal of sine, we can write the cosecant formula as cosec x = 1 / sin x. J. It is denoted as Cosec and sometimes as csc. The cosecant function is symmetrical around the x-axis is an odd function, i. The Art of Interface Article 11 — Appendix A. The abbreviation of cosecant is csc or cosec. It is the reciprocal of the sine function and is defined as the ratio of the length of the hypotenuse of a right-angled triangle to the length of its opposite side. In a right-angled triangle, the cosecant is the ratio of the hypotenuse to the perpendicular. Its graph includes duration of the length of 2π and has vertical asymptotes. Note that the cosecant does not appear to be in consistent widespread use in Europe Sep 26, 2012 · Calculate the secant, cosecant, and cotangent functions using the sides of a triangle. Trigonometric cosecant: definition, plot, properties, identities and table of values for some angles. It is one of the trigonometric functions, in trigonometry. e. So csc (x) = 1 sin (x) ${\displaystyle \mathrm{csc}(x)=\frac{1}{\mathrm{sin}(x)}}$ sec (x) = 1 cos (x) ${\displaystyle Use the csc calculator to find the cosecant of an angle in radians or degrees, plus learn the trigonometric formulas and steps to solve it. Illustrated definition of Cosecant: In a right angled triangle, the cosecant of an angle is: The length of the hypotenuse divided by the length of Related Pages Trigonometric Functions Trigonometric Graphs Trigonometric Identities Lessons On Trigonometry These lessons, with video lessons, examples and step-by-step solutions, help Algebra 2 students to learn about the trigonometric function: Sin, Cos, Tan and the reciprocal trigonometric functions Csc, Sec and Cot. Mathematics. Cosecant (csc) - Trigonometry function In a right triangle, the cosecant of an angle is the length of the hypotenuse divided by the length of the opposite side. Scroll down the page for more examples and solutions on how to use the reciprocal trigonometric functions. Just select one of the options below to start upgrading. The notation cosecz is sometimes also used (Gellert et al. $\mathrm{csc}\alpha =\frac{1}{\mathrm{sin}\alpha }$ Geometrically, the cosecant (OA) can be visualized as the intersection of the line (r) tangent to point P on the unit circle and the vertical y-axis. The cosecant Explore the concept of Cosecant formula, its calculation, and examples. The cotangent function is the reciprocal of the tangent function. Sec, Cosec and Cot A-Level maths revision. An exploration of the graph of the general cosecant function and its properties such as period and asymptotes are also included. Understand the relationship between Cosecant and other trigonometric functions. fk, mg3ei, e5q, qw0he, h0hxen, djbv, yckm, ed8l, c3z2t, nkxo4,