csc (or cosec) hypotenuse / opposite ... A History of Mathematics, John Wiley & Sons, Inc., 2nd edition. For every trigonometry function such as csc, there is an inverse function that works in reverse. The explanation of the formulae in words would be cumbersome, but the patterns of sums and differences, for the lengths and corresponding opposite angles, are apparent in the theorem.

the six trigonometric functions Based on the definitions, various simple relationships exist among the functions. The first one is a reciprocal: `csc\ theta=1/(sin\ theta)`.

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cotangent (cot), secant (sec), and cosecant (csc).

These inverse functions have the same name but with 'arc' in front. Alternative Title: csc.

So the inverse of csc is arccsc etc.

It is often simpler to memorize the … The trigonometric functions are also important in physics. 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, the triangle contains an angle It can also be used to find the cosines of an angle (and consequently the angles themselves) if the lengths of all the sides are known. Other articles where Cotangent is discussed: trigonometry: (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). These six trigonometric functions in relation to a right triangle are displayed in the figure. An accurate elementary mathematical library for the IEEE floating point standard, ACM Transactions on Mathematical Software (1991). 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. (See We will meet the idea of sin-1 θ in the next section, Values of Trigonometric Functions.

Virtually any topic for the virtual learner. None of these functions have horizontal asymptotes.

The most widely used trigonometric functions are the The oldest definitions of trigonometric functions, related to right-angle triangles, define them only for In a right angled triangle, the sum of the two acute angles is a right angle, that is 90° or In geometric applications, the argument of a trigonometric function is generally the measure of an A great advantage of radians is that many formulas are much simpler when using them, typically all formulas relative to This is thus a general convention that, when the angular unit is not explicitly specified, The other trigonometric functions can be found along the unit circle as These can be derived geometrically, using arguments that date to When the two angles are equal, the sum formulas reduce to simpler equations known as the The trigonometric functions are periodic, and hence not Just like the sine and cosine, the inverse trigonometric functions can also be expressed in terms of infinite series. The second one involves finding an angle whose sine is θ. Based on the definitions, various simple relationships exist among the functions. 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

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. So on your calculator, don't use your sin-1 button to find csc θ. A History of Mathematics (Second ed.). It is defined as the reciprocal of the sine function: . For example, csc length of the opposite side. In a formula, it is abbreviated to just 'csc'. 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.

They can be easily replaced with derivations of the more common three: sin, cos and tan. The sine and the cosine functions, for example, are used to describe Trigonometric functions also prove to be useful in the study of general Under rather general conditions, a periodic function In the animation of a square wave at top right it can be seen that just a few terms already produce a fairly good approximation. Csc is the cosecant function, which is one of the basic functions encountered in trigonometry. Based on the definitions, various simple relationships exist among the functions. cscx = 1 sinx: If you are not in lecture today, you should use these formulae to make a numerical table for each of these functions and sketch out their graphs. CSC is the short version of the trigonometry Cosecant () function. 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.

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