Grasp the following points: 1. The advantage of understanding radian system to represent angles is that the set of angles corresponds to the set of real numbers one by one. Second, trigonometric functions can be regarded as functions with real numbers as independent variables. 2. We should distinguish the concepts of positive angle, negative angle, zero angle, acute angle, obtuse angle, interval angle, quadrant angle, terminal side homoclinic angle, etc. 3. When the trigonometric function value of an angle is known, find the angle. And get the corresponding values of different quadrants. When simplifying triangle by inductive formula, we should pay attention to the choice of symbols in the formula. 4. The trigonometric function line in the unit circle is the geometric representation of trigonometric function. It is much better to use the value of trigonometric function line instead of trigonometric function value than to use the ratio specified in the definition of trigonometric function to get trigonometric function value. So trigonometric function is a powerful tool to discuss the properties of trigonometric function. 5. Be good at transforming formulas of trigonometric functions into a "standard formula" containing only one trigonometric function as far as possible, and then we can get the maximum, minimum positive period, monotonicity and so on. Some compound trigonometric functions. Special attention should be paid to maintaining the invariance of the definition domain when the function formula is deformed by constants. 6. Consider the monotonicity of the function in a given interval. Only two function values belonging to the same monotonous aspect of the same function can be compared by its monotonicity. 7. For a function with periodicity, we only need to image it in one period, and then use periodicity to image the whole function.

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8. For the proportional formula, we should be good at deformation and simplify it with the proportional triangle formula. Pay attention to the following points when reviewing: 1. To master the formulas of trigonometric functions of harmony, difference, multiplication and half angle. In the review, we should pay attention to the following common methods and simple skills of triangle equivalent deformation. ① Constant replacement, especially the replacement of "1", such as: etc. ② Division of terms and matching of angles. ③ Degree of decline and rise. ④ Universal substitution. In addition, pay attention to understand the essence of angles in the formulas of sum, difference, times and half angles of two angles. The angle in the formula can be regarded as a whole form, which can be integrated into other variables or functions to increase the application scope and strength of the formula. 2. You should be able to use sum-difference product and sum-difference formula. For trigonometric functions and difference formulas, you should introduce auxiliary angles into the form of merging, in which the quadrant where the auxiliary angle is located is determined by symbols and the value of the angle is determined. We must strengthen training and deepen our understanding of this idea.

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3. Summarize and master the common methods and skills of trigonometric function simplification and evaluation. ① When simplifying trigonometric functions, under the requirements of topic design, we should first make rational use of relevant formulas, minimize the number of angles, minimize the number of trigonometric functions, and try to achieve the same angle with the same name. Other ideas include: making the same degree different, making the higher degree lower, making the chord or tangent bigger, making the sum and difference a product, and making the product a sum. The other is the problem of finding the angle of a given value. All of them are related to formulas of trigonometric functions of evaluation, formulas of trigonometric functions of special angle and formulas of trigonometric functions of known value through appropriate transformation. When choosing formulas, we should pay attention to directionality and flexibility, create opportunities to eliminate or reduce terms, and simplify the problem. 4. formulas of trigonometric functions's simple proof. The proof of trigonometric identities can be divided into two types: without additional conditions and with additional conditions, and the proof methods are flexible and diverse. The general rule is

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① Unconditional proof of trigonometric identities: synthesis method, analytical method and mathematical induction can also be used under certain conditions. ② Proof of trigonometric identities with additional conditions: The key is to properly and timely use additional conditions, that is, to carefully find the internal relationship between additional conditions and the equation to be proved. The commonly used methods are substitution method and elimination method. When proving trigonometric identities, we should focus on learning the mutual formulas of sum, difference and product, and master the ideas and variables of equivalent transformation. Find the connection-choose the appropriate formula to find the connection between the differences; Reasonable transformation promotes contact and creatively applies basic formulas. Generally speaking, to prove angle identities or conditional identities, it is necessary to prove that trigonometric functions with the same name have equal values, that is, to prove that they are in the same monotonous interval of trigonometric functions, and then to obtain the monotonicity of functions. 5. The definition of acute trigonometric function, Pythagorean theorem, sine theorem and cosine theorem are commonly used tools when solving problems about triangles. Note the triangle area formula. 6. The common methods for finding the maximum value of trigonometric function are collocation method, discriminant method, important inequality method, variable substitution method, monotonicity and boundedness of trigonometric function, etc. Its basic idea is to transform the maximum value of trigonometric function into the maximum value of algebraic function. The concept of trigonometric function, the basic relationship and inductive formula of trigonometric function with the same angle.