The antiderivative of a trigonometric function is an alternative way of deducing the integral of the function, according to educators at Massachusetts Institute of Technology. The integral of the function is basically the derivative backwards. In the case of trigonometric functions, the antiderivative of a trigonometric identity is its derivative reverse.
University of California at Davis provides the example of the derivative of sin(x) as cos(x). To find the antiderivative of cos(x), go backwards from D(sin x) = cos(x), making the antiderivative of cos(x) to be sin(x) and some constant C. Princeton University notes that this constant C, known as the constant of integration, is essential when describing the integral of a trigonometric function because the antiderivative of cos(x) can be sin(x) + 5 or sin(x) + 5 million. To account for the constant with a derivative of zero, the constant of derivation is implemented to describe all possible constants that follow the plus sign of the integral of the function.
University of California at Davis elaborates that the pattern of the antiderivative or integral of a trigonometric identity is its derivative backwards. Further examples include the derivative of cos(x) = -sin(x), thus making the antiderivative of sin(x) to be -cos(x).