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The absolute value is necessary to compensate for both negative and positive values of the arcsecant and arccosecant functions. The signum function is also necessary due to the absolute values in the derivatives of the two functions, which create two
The following is a list of indefinite integrals (antiderivatives) of expressions involving the inverse trigonometric functions.For a complete list of integral formulas, see lists of integrals.
This allows the two congruent purple-outline triangles and to be constructed, each with hypotenuse and angle at their base. The sum of the heights of the red and blue triangles is sin θ + sin φ {\displaystyle \sin \theta +\sin \varphi } , and this is equal to twice the height of one purple triangle, i.e. 2 sin p cos q ...
It is defined everywhere except for non-positive real values of the variable, for which two different values of the logarithm reach the minimum. For all inverse hyperbolic functions, the principal value may be defined in terms of principal values of the square root and the logarithm function.
Sec-1, SEC-1, sec-1, or sec −1 may refer to: . sec x−1 = sec(x)−1 = exsec(x) or exsecant of x, an old trigonometric function; sec −1 y = sec −1 (y), sometimes interpreted as arcsec(y) or arcsecant of y, the compositional inverse of the trigonometric function secant (see below for ambiguity)
1.1 Values of the arcsecant function. 3 comments. 1.2 Limit of an (infinite) sum, and teaching a man how to fish. 15 comments. 1.3 Definition of Division. 2 comments.
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2.2 The unit circle and common trigonometric values. 3 Trigonometric functions of real or complex variables. ... arcsecant: y = arcsec(x) x = sec(y) x ≤ −1 or 1 ...