Power function isomorphism, exponential function isomorphism, sine function isomorphism, cosine function isomorphism, inverse trigonometric function isomorphism, bictangent, secant isomorphism of conic curve, isomorphism inversion.

The power function is introduced as follows:

Power function is one of the basic elementary functions. When α is an integer, the positive and negative parity of α determines the monotonicity of the function: when α is a positive odd number, the image monotonically increases in the domain of R; When α is a positive even number, the image monotonically decreases in the second quadrant and monotonically increases in the first quadrant.

The isomorphism of exponential function is introduced as follows:

Exponential function is one of the important basic elementary functions. Generally speaking, the function of y = a x (a is constant and a >；; 0, a≠ 1) is called exponential function, and the definition domain of the function is R. Note that in the definition expression of exponential function, the coefficient before a x must be the number 1, and the independent variable X must be in the exponential position, and it cannot be other expressions of X, otherwise it is not an exponential function.

Exponential function is an important function in mathematics. This function applied to the value e is written as exp(x). It can also be written as ex, where e is a mathematical constant and the base of natural logarithm, which is about equal to 2.7 1828 1828, also known as Euler number.

The sine function is introduced as follows:

Sine, a mathematical term, is a kind of trigonometric function. In a right triangle, the ratio of the opposite side to the hypotenuse of any acute angle ∠A is called the sine of ∠A, which is abbreviated from the English word sine, that is, the opposite side/hypotenuse of Sina = ∠ A.

In ancient times, the "string" in "hook, three strands, four strings and five" was the hypotenuse of a right triangle, and "hook" and "strand" were the two right-angled sides of a right triangle. Sine is the ratio of strands to chords, and cosine is the ratio of remaining right angles to chords.

Put the Pythagorean line in the circle. A chord is a line connecting two points on a circle. The largest chord is the diameter. If the chord of a right triangle is placed on the diameter, the chord is the inverse chord of ∠A, that is, sine, and the hook is the remaining chord-cosine.