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Or, "the arc whose cosine is x" is the same as "the angle whose cosine is x", because the length of the arc of the circle in radii is the same as the measurement of the angle in radians. [5] In computer programming languages, the inverse trigonometric functions are often called by the abbreviated forms asin, acos, atan. [6]
Ptolemy's theorem states that the sum of the products of the lengths of opposite sides is equal to the product of the lengths of the diagonals. When those side-lengths are expressed in terms of the sin and cos values shown in the figure above, this yields the angle sum trigonometric identity for sine: sin(α + β) = sin α cos β + cos α sin β.
Even with a calculator or computer, round-off errors make it advisable to use the sin 2 formula for small θ. Another historical advantage of the versine is that it is always non-negative, so its logarithm is defined everywhere except for the single angle ( θ = 0, 2 π , …) where it is zero—thus, one could use logarithmic tables for ...
The opposite side is the side that is opposite to angle A. The terms perpendicular and base are sometimes used for the opposite and adjacent sides respectively. See below under Mnemonics. Sine (denoted sin), defined as the ratio of the side opposite the angle to the hypotenuse.
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 that is 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 ...
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)
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.