(1) Any angle and radian

Understand the concept of arbitrary angle and radian system, and realize the conversion between radian and angle.

(2) Trigonometric function

① Understand the definition of trigonometric functions (sine, cosine and tangent) with the help of the unit circle.

② Derive inductive formulas (sine, cosine and tangent) with the help of trigonometric function lines in the unit circle, and draw pictures to understand the periodicity of trigonometric functions.

③ Understand the properties of sine function, cosine function and tangent function (such as monotonicity, maximum and minimum value, image intersecting with X axis, etc.). ) with the help of images.

④ Understand the basic relationship of trigonometric functions with the same angle:

⑤ Understand the practical significance with concrete examples; With the help of the image drawn by calculator or computer, we can observe the influence of parameters a and ω on the change of function image.

⑥ trigonometric function can be used to solve some simple practical problems, and it is recognized that trigonometric function is an important function model to describe periodic changes. (about 12 class hours)

The Practical Background and Basic Concepts of (1) Plane Vector

Through the analysis of force and other examples, we can understand the actual background of vector, the meaning of plane vector and vector equality, and the geometric representation of vector.

(2) Linear operation of vectors

① Master the operation of vector addition and subtraction and understand its geometric meaning.

(2) Master the operation of vector multiplication and understand its geometric meaning and the meaning of two vector lines.

③ Understand the linear operation properties of vectors and their geometric significance.

(3) The basic theorem and coordinate representation of plane vector.

① Understand the basic theorem of plane vector and its significance.

② Master the orthogonal decomposition of plane vector and its coordinate representation.

③ Coordinates will be used to represent the addition, subtraction and multiplication of plane vectors.

(4) understand the condition that the plane vector * * * straight line is represented by coordinates.

(4) the product of plane vectors

① Understand the meaning and physical meaning of the product of plane vectors through examples such as "work" in physics.

② Understand the relationship between the product of plane vector and vector projection.

(3) Grasp the coordinate expression of the product of quantity, and carry out the product operation of plane vector.

(4) The included angle between two vectors can be expressed by the product of quantities, and the vertical relationship between two plane vectors can be judged by the product of quantities.

(5) Application of carrier

Through the process of solving some simple plane geometric problems, mechanical problems and other practical problems with vector method, I realize that vector is a tool to deal with geometric and physical problems and cultivate the ability to calculate and solve practical problems. (about 8 class hours)

(1) experienced the process of deriving the cosine formula of the difference between two angles by using the product of vectors, and further realized the function of vector method.

(2) Sine, cosine and tangent formulas of sum and difference of two angles and sine, cosine and tangent formulas of two angles can be derived from cosine formula of difference of two angles, so as to understand their internal relations.

(3) We can use the above formula to carry out simple identity transformation (including guiding and deducing product sum and difference, product sum and difference, and half-angle formula, but we don't need to remember).