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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 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 of the ...
cos x−1 = cos(x)−1 = −(1−cos(x)) = −ver(x) or negative versine of x, the additive inverse (or negation) of an old trigonometric function; cos −1 y = cos −1 (y), sometimes interpreted as arccos(y) or arccosine of y, the compositional inverse of the trigonometric function cosine (see below for ambiguity)
In keeping with the general notation, some English authors use expressions like sin −1 (x) to denote the inverse of the sine function applied to x (actually a partial inverse; see below). [8] [6] Other authors feel that this may be confused with the notation for the multiplicative inverse of sin (x), which can be denoted as (sin (x)) −1. [6]
The polynomials, exponential function e x, and the trigonometric functions sine and cosine, are examples of entire functions. Examples of functions that are not entire include the square root, the logarithm, the trigonometric function tangent, and its inverse, arctan. For these functions the Taylor series do not converge if x is far from b.
sinh x is half the difference of e x and e −x cosh x is the average of e x and e −x. In terms of the exponential function: [1] [4]. Hyperbolic sine: the odd part of the exponential function, that is, = = =.
cis is a mathematical notation defined by cis x = cos x + i sin x, [nb 1] where cos is the cosine function, i is the imaginary unit and sin is the sine function. x is the argument of the complex number (angle between line to point and x-axis in polar form).
Fig. 1 – A triangle. The angles α (or A), β (or B), and γ (or C) are respectively opposite the sides a, b, and c.. In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles.
The sinc function as audio, at 2000 Hz (±1.5 seconds around zero) In mathematics, the historical unnormalized sinc function is defined for x ≠ 0 by = .. Alternatively, the unnormalized sinc function is often called the sampling function, indicated as Sa(x).