Difference between revisions of "Cosine"
From specialfunctionswiki
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[[Relationship between cosine, Gudermannian, and sech]]<br /> | [[Relationship between cosine, Gudermannian, and sech]]<br /> | ||
[[Relationship between sech, inverse Gudermannian, and cos]]<br /> | [[Relationship between sech, inverse Gudermannian, and cos]]<br /> | ||
| + | [[2cos(mt)cos(nt)=cos((m+n)t)+cos((m-n)t)]]<br /> | ||
=See Also= | =See Also= | ||
Revision as of 22:03, 19 December 2017
The cosine function, $\cos \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by the formula $$\cos(z)=\dfrac{e^{iz}+e^{-iz}}{2},$$ where $e^z$ is the exponential function.
Graph of $\cos$ on $[-2\pi,2\pi]$.
Domain coloring of $\cos$.
Trig functions diagram using the unit circle.
Properties
Derivative of cosine
Taylor series of cosine
Weierstrass factorization of cosine
Beta in terms of sine and cosine
Relationship between cosine and hypergeometric 0F1
Relationship between spherical Bessel y and cosine
Relationship between cosh and cos
Relationship between cos and cosh
Relationship between cosine, Gudermannian, and sech
Relationship between sech, inverse Gudermannian, and cos
2cos(mt)cos(nt)=cos((m+n)t)+cos((m-n)t)
See Also
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 4.3.2
