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[1] [10] Another precarious convention used by a small number of authors is to use an uppercase first letter, along with a “ −1 ” superscript: Sin −1 (x), Cos −1 (x), Tan −1 (x), etc. [11] Although it is intended to avoid confusion with the reciprocal, which should be represented by sin −1 (x), cos −1 (x), etc., or, better, by ...
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
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) cos −1 x = cos −1 (x), sometimes interpreted as (cos(x)) −1 = 1 / cos(x) = sec(x) or secant of x, the multiplicative inverse (or reciprocal) of the trigonometric ...
The red section on the right, d, is the difference between the lengths of the hypotenuse, H, and the adjacent side, A.As is shown, H and A are almost the same length, meaning cos θ is close to 1 and θ 2 / 2 helps trim the red away.
The points labeled 1, Sec(θ), Csc(θ) represent the length of the line segment from the origin to that point. Sin(θ), Tan(θ), and 1 are the heights to the line starting from the x-axis, while Cos(θ), 1, and Cot(θ) are lengths along the x-axis starting from the origin.
The exsecant and versine functions substitute for the expressions exsec x = sec x − 1 and vers x = 1 − sec x which appear frequently in certain applications. [1] The names exsecant, versine, chord, etc. can also be applied to line segments related to a circular arc. [2]
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) sec −1 x = sec −1 (x), sometimes interpreted as (sec(x)) −1 = 1 / sec(x) = cos(x) or cosine of x, the multiplicative inverse (or reciprocal) of the trigonometric ...
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). The notation is less commonly used in mathematics than Euler's formula, e ix, which ...