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# Cofunction

[koh-fuhngk-shuhn]
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"):

$sin\left(frac\left\{pi\right\}\left\{2\right\} - A\right) = cos\left(A\right)$ $cos\left(frac\left\{pi\right\}\left\{2\right\} - A\right) = sin\left(A\right)$

The same is true of secant and cosecant and of tangent and cotangent:

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

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

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