Difference between revisions of "Tangent"

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The tangent function is defined as the ratio of the [[sine]] and [[cosine]] functions:
 
The tangent function is defined as the ratio of the [[sine]] and [[cosine]] functions:
$$\tan(x) = \dfrac{\sin(x)}{\cos(x)}.$$
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$$\tan(z) = \dfrac{\sin(z)}{\cos(z)}.$$
  
[[File:Tangent.png|500px]]
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<div align="center">
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<gallery>
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File:Tangentplot.png|Graph of $\tan$ over $[-2\pi,2\pi]$.
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File:Complextangentplot.png|[[Domain coloring]] of $\tan$.
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File:Trig Functions Diagram.svg|Trig functions diagram using the unit circle.
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</gallery>
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</div>
  
[[File:Complex tan.jpg|500px]]
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=Properties=
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[[Derivative of tangent]]<br />
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[[Relationship between tan and tanh]]<br />
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[[Relationship between tanh and tan]]<br />
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[[Relationship between tangent, Gudermannian, and sinh]]<br />
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[[Relationship between sinh, inverse Gudermannian, and tan]]<br />
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=See Also=
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[[Arctan]] <br />
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[[Tanh]] <br />
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[[Arctanh]] <br />
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=References=
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* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Cosine|next=Cosecant}}: 4.3.3
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{{:Trigonometric functions footer}}
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[[Category:SpecialFunction]]

Latest revision as of 03:38, 6 July 2016

The tangent function is defined as the ratio of the sine and cosine functions: $$\tan(z) = \dfrac{\sin(z)}{\cos(z)}.$$

Properties

Derivative of tangent
Relationship between tan and tanh
Relationship between tanh and tan
Relationship between tangent, Gudermannian, and sinh
Relationship between sinh, inverse Gudermannian, and tan

See Also

Arctan
Tanh
Arctanh

References

Trigonometric functions