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In trigonometry, the tangent of an angle in a right triangle is defined as the ratio of the opposite and adjacent sides. The tangent is a trigonometric function of the angle and is often abbreviated tan.

There is a relationship between the tangent and the sine and cosine functions:

\tan \theta = \frac{\sin \theta}{\cos \theta} = \cot \left(\frac{\pi}{2} - \theta \right) = \frac{1}{\cot \theta} \,

Tangent Graph

The basic tangent graph is as follow:

x values y values
-π/2 undefined
-π/4 -1
0 0
π/4 1
π/2 undefined

That would be a full period of the graph - as 2π radians is equivalent to one circle. The graph continues in that pattern.

Other Uses

In analytic geometry, a line which intersects a circle or curve at only one point is said to be tangent to that circle or curve. At the point of intersection, the curve and the line have exactly the same slope.

Compare: Asymptote

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