# Representations of Trigonometric and Hyperbolic Functions in Terms of Sector Areas

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A sector of angle of a unit circle has an area equal to radians. So half the area can serve as the argument for the trigonometric functions via parametric equations for and . The two constructions shown are consistent with the trigonometric identities and . (As a consequence, circular functions are alternatively called trigonometric functions.)

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Contributed by: S. M. Blinder (August 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The thumbnail and the third snapshot show the comparative behavior of corresponding trigonometric and hyperbolic functions.

Reference

[1] S. M. Blinder, *Guide to Essential Math*, Amsterdam: Elsevier Academic Press, 2008, pp. 71–72, 188–189.

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