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In mathematics, a function f is cofunction of a function g if f(A) = g(B) whenever A and B are complementary angles. This definition typically applies to trigonometric functions.[1]

For example, sine and cosine are cofunctions of each other (hence the "co" in "cosine"):
\( \sin\left(\frac{\pi}{2} - A\right) = \cos(A) \cos\left(\frac{\pi}{2} - A\right) = \sin(A)\)

The same is true of secant and cosecant and of tangent and cotangent:
\( \sec\left(\frac{\pi}{2} - A\right) = \csc(A) \csc\left(\frac{\pi}{2} - A\right) = \sec(A) \)
\( \tan\left(\frac{\pi}{2} - A\right) = \cot(A) \cot\left(\frac{\pi}{2} - A\right) = \tan(A) \)

These equations are also known as the cofunction identities.[1]

References

Aufmann, Richard; Nation, Richard (2014), Algebra and Trigonometry (8th ed.), Cengage Learning, p. 528, ISBN 9781285965833.

Undergraduate Texts in Mathematics

Graduate Texts in Mathematics

Graduate Studies in Mathematics

Mathematics Encyclopedia

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