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The orange sheet in the middle is the principal sheet representing arctan x. The blue sheet above and green sheet below are displaced by 2 π and −2 π respectively. Since the inverse trigonometric functions are analytic functions , they can be extended from the real line to the complex plane.
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.
For example, the sine of angle θ is defined as being the length of the opposite side divided by the length of the hypotenuse. The six trigonometric functions are defined for every real number , except, for some of them, for angles that differ from 0 by a multiple of the right angle (90°).
The coversed cosine [26] or covercosine, abbreviated covercosin, covercos, or cvc In full analogy to the above-mentioned four functions another set of four "half-value" functions exists as well: The haversed sine [ 27 ] or haversine (Latin semiversus ), [ 28 ] [ 29 ] abbreviated haversin , semiversin , semiversinus , havers , hav , [ 30 ] [ 31 ...
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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.
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