Cofunction

Sine and cosine are each others' cofunctions.

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]

This also holds true for the coversine (coversed sine, cvs), covercosine (coversed cosine, cvc), hacoversine (half-coversed sine, hcv), hacovercosine (half-coversed cosine, hcc) and excosecant (exterior cosecant, exc):

$\operatorname{cvs}\left(\frac{\pi}{2} - A\right) = \operatorname{ver}(A)$

$\operatorname{cvc}\left(\frac{\pi}{2} - A\right) = \operatorname{vcs}(A)$

$\operatorname{hcv}\left(\frac{\pi}{2} - A\right) = \operatorname{hav}(A)$

$\operatorname{hcc}\left(\frac{\pi}{2} - A\right) = \operatorname{hvc}(A)$

$\operatorname{exc}\left(\frac{\pi}{2} - A\right) = \operatorname{exs}(A)$

See also

• Vercosine (versed cosine)
• Havercosine (half-versed cosine)
• Covariance

References

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