First, the most valuable classic topic of junior high school mathematics fermat point

Fermat point, also known as Torricelli point, is a famous extreme problem of "finding the minimum sum of the distances from a point to three vertices of a triangle".

Second, the problem of Hu Bugui's classical maximum in junior high school mathematics.

Hu Bugui is another classic extreme value problem. "Hu Bugui, why did you come back?" This mathematical maximum problem has been circulating for a long time, and sine trigonometric function is usually constructed to transform line segments, thus solving the problem.

Third, the maximum problem of junior high school mathematics classics-Ashby's circle problem.

Albert Circle and Hu Bugui have the same effect. Hu Bugui usually constructs sine trigonometric function to transform line segments, and Albert circle usually constructs similar triangles to transform line segments.

Fourth, the "one arrow through the heart" model of the classical maximum problem of junior high school mathematics

The "one arrow through the heart" model in the maximum problem does not exist in isolation. It is usually integrated with the hidden circle model with strings and circles and the general horse drinking model.

Verb (abbreviation of verb) matching method

When the function expression only contains sine or cosine functions, and their highest degree is 2, we can solve the problem of transforming a given function into the maximum value of a quadratic function by formula or substitution.

Six, the combination of number and shape method

For sin? x+cos？ X= 1, so the point (cosx, sinx) is on the unit circle, and the geometric method of combining numbers and shapes can be considered to solve the maximum problem of trigonometric function of sine sinx and cosine cosx.