## Complementary function to sin(x)

### The complementary function to sin(x) is cos(x)

The complementary function to sin(x) is cos(x). In mathematics, complementary functions are pairs of functions that sum up to a constant value. In the context of trigonometric functions, the sine and cosine functions are complementary.

The sine function (sin(x)) describes the ratio of the length of the side opposite to an angle in a right triangle to the length of the hypotenuse. It reaches its maximum value of 1 when the angle is 90 degrees (or π/2 radians) and decreases as the angle increases or decreases.

The cosine function (cos(x)), on the other hand, describes the ratio of the length of the adjacent side to the hypotenuse in a right triangle. It reaches its maximum value of 1 when the angle is 0 degrees (or 2π radians) and also when the angle is 360 degrees (or 2π radians). The cosine function is the complementary function to the sine function, meaning that their sum is always equal to 1.

So, if we have sin(x) as the given function, then the complementary function would be cos(x). Their sum sin(x) + cos(x) = 1 is a constant value.

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