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Cofunction

  

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(frac{pi}{2} - A) = cos(A) cos(frac{pi}{2} - A) = sin(A)

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

sec(frac{pi}{2} - A) = csc(A) csc(frac{pi}{2} - A) = sec(A)

tan(frac{pi}{2} - A) = cot(A) cot(frac{pi}{2} - A) = tan(A)

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

See also

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Last updated on Monday September 08, 2008 at 22:20:38 PDT (GMT -0700)
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