Difference between revisions of "Sine"

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=Definition=
 
 
The sine function $\sin \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by
 
The sine function $\sin \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by
 
$$\sin(z)=\dfrac{e^{iz}-e^{-iz}}{2i},$$
 
$$\sin(z)=\dfrac{e^{iz}-e^{-iz}}{2i},$$

Revision as of 17:34, 1 July 2017


The sine function $\sin \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by $$\sin(z)=\dfrac{e^{iz}-e^{-iz}}{2i},$$ where $e^{iz}$ denotes the exponential.

Properties

Derivative of sine
Pythagorean identity for sin and cos
Taylor series of sine
Weierstrass factorization of sine
Euler's reflection formula for gamma
Beta in terms of sine and cosine
Relationship between sine and hypergeometric 0F1
Relationship between spherical Bessel j sub nu and sine
Relationship between sin and sinh
Relationship between sinh and sin
Relationship between sine, Gudermannian, and tanh
Relationship between tanh, inverse Gudermannian, and sin

Videos

[1]

See Also

Arcsin
Arcsinh
Cosecant
Sinh

External links

The sine product formula and the gamma function

References

Trigonometric functions