Key Test Site of Trigonometric Function in College Entrance Examination (1)
Study on the Properties of Functions from Analytic Expressions
Common test sites:
Find the minimum positive period of the function, the maximum value of the function in a certain interval, the monotone interval of the function, the parity of the function, the equation of the symmetry center and axis, the transformation relationship between the given function and the image with y=sinx, etc.
For these problems, it is generally necessary to transform the resolution function into the form of y=Asin(ωx+φ) by trigonometric constant transformation formula, and then get the corresponding results.
In this process, the function is generally transformed into the form of asin Ω x+bcos Ω x by using induction formula, double angle formula and sum-difference identity of two angles (the ratio of two coefficients A and B is 1: 1), and then transformed by using auxiliary angle formula.
College entrance examination mathematics trigonometric function key kaodian
College Entrance Examination Mathematics Trigonometric Function Key Test Site (2)
Determine the resolution function according to the conditions.
This kind of problems often give the image of the function, and find the resolution function y = asin (ω x+φ)+b.
a =(max-min)/2；
B= (max+min)/2;
The period t of the function is obtained by observation (mainly determined by the distance between the maximum point and the minimum point and the abscissa of the "equilibrium point"), and then ω is obtained by using the period formula T=2π/ω;
Use special points (such as highest point, lowest point, intersection point with X axis, points with special coordinates on the image, etc.). ) find a φ';
Finally, the inductive formula is used to form an analytical formula that meets the requirements.
College entrance examination mathematics trigonometric function key kaodian
College entrance examination mathematics key kaodian
Test center 1: set and simple logic
The collection part generally appears in the form of multiple-choice questions, which belongs to easy questions. The key point is to know and understand the relationship between sets. In recent years, the examination questions have strengthened the examination of the simplification ability of set calculation, and developed to the infinite set to examine the abstract thinking ability. When solving these problems, we should pay attention to the intuition of geometry and the transformation and simplification of set representation method. There are two forms of simple logical examination: one is to directly examine propositions and their relations, logical conjunctions, "necessary and sufficient relations", to judge the truth value of propositions, and to deny full-name propositions and proper-name propositions. In answering questions, the other is to thoroughly examine the mathematical problem-solving process and logical reasoning expressed by common logical terms.
Test Site 2: Functions and Derivatives
Function is the key content of college entrance examination. Taking multiple-choice questions and fill-in-the-blank questions as carriers, the definition and scope of functions, the nature of functions, functions and equations, and the application of basic elementary functions (linear and quadratic functions, exponential, logarithmic and power functions). , the score is about 10, and the problem-solving and derivative encounter function.