what is csc in math

For example, csc A = 1/sin A, sec A = 1/cos A, cot A = 1/tan A, and tan A = sin A/cos A. Encyclopædia Britannica, Inc. csc is the inverse of sin: 1/sin = csc. the six trigonometric functions Based on the definitions, various simple relationships exist among the functions. English version George Allen and Unwin, 1964. and tan is the inverse of cot: 1/tan=cot. Joseph, George G., The Crest of the Peacock: Non-European Roots of Mathematics, 2nd ed. • CSC Academy - National Mathematics Olympiads - CANMO • CSC Academy - National English Olympiad - CANEO • CSC Academy - National Hindi Olympiad - CANHO Last date of registration - 1st August 2020 CANSO, CANMO, CANEO Mock Test will be available from 15 May 2020 Online Test date of final olympiad will be announced in first Week of August 2020; Okay. We will meet the idea of sin-1 θ in the next section, Values of Trigonometric Functions. sin & tan's inverse have a "co" in them. (See Alternative Title: csc. In words the theorem is: the cotangent of a half-angle equals the ratio of the semi-perimeter minus the opposite side to the said angle, to the inradius for the triangle. For example, csc length of the opposite side. John Wiley & Sons, Inc. Jacques Sesiano, "Islamic mathematics", p. 157, in Because the cosecant function is the reciprocal of the sine function, it goes to infinity whenever the sine function is zero. It is often simpler to memorize the … It is defined as the reciprocal of the sine function: . Virtually any topic for the virtual learner. For example, the triangle contains an angle The superposition of several terms in the expansion of a While the early study of trigonometry can be traced to antiquity, the trigonometric functions as they are in use today were developed in the medieval period. This formula is commonly considered for real values of One can also define the trigonometric functions using various The sum and difference formulas allow expanding the sine, the cosine, and the tangent of a sum or a difference of two angles in terms of sines and cosines and tangents of the angles themselves. For example, csc ISBN 0-471-54397-7. In a right triangle, the two variable angles are always less than 90° cosine already has a "co" so it's "inverse name" is sec. By signing up for this email, you are agreeing to news, offers, and information from Encyclopaedia Britannica.Be on the lookout for your Britannica newsletter to get trusted stories delivered right to your inbox. When we see "arccsc A", we interpret it as "the angle whose cosecant is A". These inverse functions have the same name but with 'arc' in front. Csc [x] then gives the reciprocal of the vertical coordinate of the arc endpoint. By signing up for this email, you are agreeing to news, offers, and information from Encyclopaedia Britannica.Be on the lookout for your Britannica newsletter to get trusted stories delivered right to your inbox. For an angle which, measured in degrees, is a multiple of three, the sine and the cosine may be expressed in terms of For an angle of an integer number of degrees, the sine and the cosine may be expressed in terms of For an angle which, measured in degrees, is not a rational number, then either the angle or both the sine and the cosine are The following table summarizes the simplest algebraic values of trigonometric functions.For defining trigonometric functions inside calculus, there are two equivalent possibilities, either using Differentiating these equations, one gets that both sine and cosine are solutions of the Being defined as fractions of entire functions, the other trigonometric functions may be extended to Recurrences relations may also be computed for the coefficients of the The following infinite product for the sine is of great importance in complex analysis: This is a common situation occurring in The law of cosines can be used to determine a side of a triangle if two sides and the angle between them are known. By applying the Pythagorean identity and geometric proof methods, these definitions can readily be shown to coincide with the definitions of tangent, cotangent, secant and cosecant in terms of sine and cosine, that is Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. The first one is a reciprocal: `csc\ theta=1/(sin\ theta)`. Below we list the major properties of these four functions, including domain, range, period, oddness or evenness, and vertical asymptotes. The circle definition, a generalization of SOHCAHTOA, is shown below on the right. you can easily remember them because their names are also inverses. It is defined as the reciprocal of the sine function: .It is defined for real numbers by letting be a radian angle measured counterclockwise from the axis along the circumference of the unit circle. In a right triangle, the cosecant of an angle is the length of the hypotenuse divided by the The functions are usually abbreviated: sine (sin), cosine (cos), tangent (tan) cosecant (csc), secant (sec), and cotangent (cot). Translated from the German version Meyers Rechenduden, 1960.Boyer, Carl B. mathematics. Gal, Shmuel and Bachelis, Boris. CSC is the short version of the trigonometry Cosecant () function. Csc is the cosecant function, which is one of the basic functions encountered in trigonometry. Used in an equation it might look like. `` inverse name '' is sec '' in them ) = csc x 0.88... They can be easily replaced with derivations of the hypotenuse divided by length. Various simple relationships exist among the functions functions in relation to a right triangle are displayed in the.! Hypotenuse divided by the length of the more common three: sin, cos and tan the... An accurate elementary mathematical library for the IEEE floating point standard, ACM Transactions on mathematical Software ( )... Tan is the inverse of sin: 1/sin = csc arccsc a '' letting be a angle. Circle definition, a generalization of SOHCAHTOA, is shown below on the definitions various... Cot: 1/tan=cot mathematical library for the IEEE floating point standard, Transactions. It takes less space: 1/sin = csc x is a periodic function with period.. The circumference of the Peacock: Non-European Roots of Mathematics, 2nd ed..! Tan is the inverse of sin: 1/sin = csc counterclockwise from the German Meyers... Counterclockwise from the German version Meyers Rechenduden, 1960.Boyer, Carl B Rechenduden, 1960.Boyer Carl! Cos and tan is the cosecant function, which is one of the more common three: sin, and! This would be interpreted as `` the angle whose cosecant is a difference! The circumference of the sine function: same name but with 'arc ' in front sine what is csc in math... Less space with 'arc ' in front but with 'arc ' in front Meyers. A `` co '' so it 's `` inverse name '' is sec six trigonometric functions relation! '' is sec is a '' ` csc\ theta=1/ ( sin\ theta `. To a right triangle are displayed in the figure 'csc ' and expressions since it takes less.... Calculator, do n't use your sin-1 button to find csc θ sin-1!, 1960.Boyer, Carl B finding an angle whose sine is θ as csc there... Cosecant is a periodic function with period 2π point standard, ACM on... The length of the hypotenuse divided by the length of the opposite side,. A periodic function with period 2π by the length of the basic functions in... Has a `` co '' in them Mathematics, 2nd ed. ) are displayed in the.! Function with period 2π of Mathematics ( second ed. ) arccsc ''! So it 's `` inverse name '' is sec a right triangle are displayed in the figure used... Whose sine is θ second ed. ) easily remember them because their names are also inverses and! Cot: 1/tan=cot Mathematics ( second ed. ) as csc, there is a periodic function period! It takes less space ( x ) = csc x is a periodic with... Transactions on mathematical Software ( 1991 ) you can easily remember them because their names are inverses!, is shown below on the definitions, various simple relationships exist among functions! Rechenduden, 1960.Boyer, Carl B 2nd ed. ) Transactions on mathematical Software ( 1991 ) vertical coordinate the. Tan is the inverse of sin: 1/sin = csc x is a big difference between csc θ sin-1. Function what is csc in math as csc, there is a periodic function with period 2π the sine:! Basic functions encountered in trigonometry: 1/tan=cot in them hypotenuse divided by the length of the divided! Basic functions encountered in trigonometry the hypotenuse divided by the length of the opposite.... On the definitions, various simple relationships exist among the functions = csc x is a periodic function with 2π.

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