1, the properties of trigonometric transformation and trigonometric function;

Roadmap to solve the problem: different keratinization, the same angle. Put down the curtains and enlarge the angle. Transform f (x) = asin (wx+φ)+H. Combining properties to solve.

Construction of answer template: simplification: simplification of trigonometric function, which is summarized as the form of y=Asin(wx+φ)+h, that is, the form of "one angle at a time, one function". Whole substitution: wx+φ is regarded as a whole, and the conditions are determined by the properties of y=sinx and y=cosx.

Solution: Find the conditional solution with the range of wx+p, get the property of function y=Asin(wx+φ)+h, and write the result. Reflection: Review, check the key points and error-prone points, predict the results, and check the standardization.

2. Solve the trigonometric function problem:

Roadmap to solve the problem: simplification and deformation; Transforming cosine theorem into edge relation: proof of deformation. Use cosine theorem to express angle; Find the range with basic inequality; Determine the value range of the angle.

Construct the answer template: determine the conditions: that is, determine what is known in the triangle and what is sought, mark it in the diagram, and then determine the direction of transformation. Fixed tools: that is, according to the conditions and requirements, the tools for transformation are reasonably selected to make the corners transform each other. Seek results.

Reflection: pay attention to the direction of transformation when implementing corner interchange. Generally, there are two ways of thinking: first, all of them are transformed into the relationship between edges; Second, all of them are transformed into the relationship between angles, and then they are deformed identically.

3. General term and sum of series:

Roadmap for solving problems: find an item first, or find the relationship of series. Find the general term formula. Find the sequence and general formula.

Construct the answer template: Recursion: Determine the relationship between two adjacent terms of a series according to known conditions, that is, find the recurrence formula of the series. Solving the general term: according to the recursive formula of the series, it is converted into the formula of arithmetic or proportional series, or the formula of solving the general term by accumulation or multiplication.

Determination method: determination summation method (such as formula method, sub-item elimination method, dislocation subtraction method, grouping method, etc.). ) According to the structural characteristics of sequence expressions. Write step: standardize write sum step. Reflection: Reflection and review, focusing on key points, making mistakes easily, and standardizing problem solving.

4. Use the space vector to find the angle:

Roadmap for solving problems: establish a coordinate system and use it to represent vectors. Coordinate operation of space vector. Find the angle and distance of space with vector tools.

Construct the answer template: find the vertical line: find (or make) three straight lines that are perpendicular to each other and have a common intersection. Write coordinates: establish a spatial rectangular coordinate system and write the coordinates of characteristic points. Find the vector: find the direction vector of a straight line or the normal vector of a plane. Find included angle: calculate the included angle of the vector. Conclusion: Find the angle between two planes or the angle between a straight line and a plane.

5. Range problem in conic curve;

Roadmap for solving problems: setting equations. Solubility coefficient. Draw a conclusion.

Construct the answer template: propose the relationship: extract the inequality relationship from the question setting conditions. Find the function: use a variable to represent the target variable and substitute it into the inequality relationship. Obtained range: the range of parameters is obtained by solving inequalities with target variables. Review again: note that the range of target variables is limited by other factors in the problem.