Cofunction

Cofunction: This article is about a mathematical term. For an entity in computer science, see Coroutine.

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.

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:

$\sec\left(\frac{\pi}{2} - A\right) = \csc(A)$ $\csc\left(\frac{\pi}{2} - A\right) = \sec(A)$

$\tan\left(\frac{\pi}{2} - A\right) = \cot(A)$ $\cot\left(\frac{\pi}{2} - A\right) = \tan(A)$

Sometimes writing a function in terms of its cofunction helps solve trigonometric equations. A simple example is the equation sin A = cos B.

See also

Trigonometric function

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