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The tangent is defined as the ratio between the sine and the cosine

and is thus a derived function.



The cosine of θ is by definition the first coordinate of the point P (x, y) on the unit circle and the sine is the second coordinate.

So the tangent is


Phase shifts


Example 1

The sin (45°) = ½√2 and the cos (45°) = ½√2, so that



The abbreviation tan was first used by the French mathematician Albert Girard (1595 - 1632).

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