The antiderivative of cos(x) is sin(x) + c, where c is an arbitrary constant. The antiderivative is more commonly called the indefinite integral. One must add an arbitrary constant into the antiderivative because sin(x) + c differentiates to cos(x) for all values of c.
The cosine function, cos(x), is defined as the ratio between the adjacent and hypotenuse edges of a right-angled triangle that includes the angle x. The cosine function is a periodic function that is the derivative of the periodic function sin(x), which is defined as the ratio between the opposite and hypotenuse edges of the triangle containing angle x.