Let f (x) = sinx; (f(x+dx)- f (x)/dx = (sin (x+dx)-sinx)/dx = (sinxcosdx+sindx-sinx)/dx, because dx approaches 0, cosdx approaches 1, (f (x+dx)-.

According to the important limit, when x approaches 0, sinx/x is equal to 1, (f (x+dx)-f (x))/dx = cosx, that is, the derivative function of sinx is cosx.

In the same way, let f (x) = cos (f (x+dx)-f (x))/dx = (cos (x+dx)-cosx)/dx = (cosxcosdx-sinxsindx-sinx)/dx, because dx approaches 0cosdx and 1 (.

According to the important limit, when x approaches 0, sinx/x is equal to1(f (x+dx)-f (x))/dx = -sinx, that is, the derivative function of cosx is-sinx.

1, trigonometric function

Trigonometric function is a kind of transcendental function in elementary function in mathematics. Their essence is the mapping between the set of arbitrary angles and a set of ratio variables. The usual trigonometric function is defined in the plane rectangular coordinate system, and its domain is the whole real number domain.

The other is defined in a right triangle, but it is incomplete.

Trigonometric functions have important applications in complex numbers. Trigonometric function is also a common tool in physics.

2. Function

Function, a mathematical term. Its definition is usually divided into traditional definition and modern definition. The essence of these two functional definitions is the same, but the starting point of narrative concept is different. The traditional definition is from the perspective of movement change, and the modern definition is from the perspective of set and mapping.

The modern definition of a function is to give a number set A, assume that the element in it is X, and apply the corresponding rule F to the element X in A, and record it as f(x) to get another number set B.

Assume that the element in B is Y, and the equivalence relation between Y and X can be expressed as y=f(x). The concept of function consists of three elements: domain A, range B and corresponding rule F, among which the core is corresponding rule F, which is the essential feature of function relationship.

Function was originally translated by Li, a mathematician of Qing Dynasty in China, in his book Algebra. He translated this way because "whoever believes in this variable is the function of that variable", that is, the function means that one quantity changes with another quantity, or that one quantity contains another quantity.