Cosine
One of the trigonometric functions:
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Its domain of definition is the entire real line; its range of values is the closed interval ; the cosine is an even periodic function (with period
). The cosine and the sine are related via the formula
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The cosine and the secant are related via the formula
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The derivative of the cosine is:
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The integral of the cosine is:
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The series expansion is:
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The inverse function is the arccosine.
The cosine and sine of a complex argument are related to the exponential function by Euler's formula:
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If is a real number, then
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If (a purely imaginary number), then
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where is the hyperbolic cosine.
Comments
A geometric interpretation of the cosine of an argument (angle) is as follows. Consider the unit circle
in the (complex) plane with origin
. Let
denote the angle between the radius (thought of as varying) and the positive
-axis. Then
is equal to the (signed) distance from the point
on
corresponding to
to the
-axis. See also Sine.
References
[1] | A.I. Markushevich, "Theory of functions of a complex variable" , 1 , Chelsea (1977) (Translated from Russian) |
Cosine. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Cosine&oldid=31900