Compulsory 4: Chapter 1, Trigonometric Function: 1. Understanding the concepts of arbitrary angle and arc system can realize the conversion between radian and angle. 2.( 1) Understand the definition of trigonometric functions (sine, cosine and tangent) at any angle with the help of the unit circle. (2) By deducing the inductive formula (π/2 α, sine, cosine and tangent of π α) from the trigonometric function line in the unit circle, we can draw the images of y=sinx, y=cosx and y=tanx, and understand the periodicity of trigonometric function. (3) Understand the relationship of trigonometric functions with the same angle: sin2α+cos2α =1tanα cotα =1(4) Understand the properties of sine function, cosine function on [0, π] and tangent function on [-π/2, π/2] with the help of images (such as monotonicity and monotonicity) (5) Understanding the practical significance of y=Asin( ωx+φ) with concrete examples; With the help of the image drawn by calculator or computer, we can observe the influence of a, ω and φ on the change of function image. (6) We can use trigonometric function to solve some practical problems and realize that trigonometric function is an important function model to describe periodic changes. Chapter 2 Plane Vector: 1. Through the analysis of force and other examples, we can understand the actual background of vector, the meaning of equality between plane vector and vector, and the geometric representation of vector. 2.( 1) Through examples, master the operation of vector addition and subtraction and understand its geometric meaning; (2) Through examples, master the operation of vector number multiplication, understand its geometric meaning and the meaning of two vector lines. (3) Understand the linear operation properties of vectors and their geometric significance. 4.( 1) Understand the meaning and physical meaning of plane vector product through examples such as "work" in physics. (2) Understand the relationship between plane vector product and vector projection. (3) Grasp the coordinate expression of the product and carry out the operation of the plane vector product. (4) The product can be used to represent the included angle between two vectors. The vertical relationship between two plane vectors is judged by the product of quantities. (5) Experience solving some simple plane geometry problems with vector method, and realize that vector is a tool to deal with geometry problems and physical problems. , cultivate the ability to calculate and solve practical problems. Chapter 3 trigonometric identity transformation: 1. Experience the process of deducing the cosine formula of the difference between two angles by the product of vectors, and further understand the function of vector method. 2. The sine, cosine and tangent formulas of the sum of two angles and the sine, cosine and tangent formulas of two angles can be derived from the cosine formula of the difference between two angles, and their internal relations can be understood. 3. Be able to use the above formula correctly for simple identity transformation (including the derivative of product and difference, the product of sum and difference, and the half-angle formula, but memory is not required). Key formula: 1) sum and difference formula of two angles (remember everything you write)
sin(A+B)=sinAcosB+cosAsinB
sin(A-B)=sinAcosB-sinBcosA？
cos(A+B)=cosAcosB-sinAsinB
cos(A-B)=cosAcosB+sinAsinB
tan(A+B)=(tanA+tanB)/( 1-tanA tanB)
tan(A-B)=(tanA-tanB)/( 1+tanA tanB)
2) From the above formula, the following double-angle formula can be derived.
tan2A=2tanA/[ 1-(tanA)^2]
cos2a=(cosa)^2-(sina)^2=2(cosa)^2 - 1= 1-2(sina)^2
(The cosine above is very important)
sin2A=2sinA*cosA
3) Half-angle just remember this:
Tan(A/2)=( 1-cosA)/ Sina = Sina /( 1+cosA)
(4) The power reduction formula can be derived from the cosine of double angle.
(sinA)^2=( 1-cos2A)/2
(cosA)^2=( 1+cos2A)/2
5) Using the above power reduction formula, the following commonly used simplified formulas can be derived.
1-cosA=sin^(A/2)*2
1-sinA=cos^(A/2)*2
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1) Formula for sum and difference of two angles (remember everything written)
sin(A+B)=sinAcosB+cosAsinB
sin(A-B)=sinAcosB-sinBcosA？
cos(A+B)=cosAcosB-sinAsinB
cos(A-B)=cosAcosB+sinAsinB
tan(A+B)=(tanA+tanB)/( 1-tanA tanB)
tan(A-B)=(tanA-tanB)/( 1+tanA tanB)
2) From the above formula, the following double-angle formula can be derived.
tan2A=2tanA/[ 1-(tanA)^2]
cos2a=(cosa)^2-(sina)^2=2(cosa)^2 - 1= 1-2(sina)^2
(The cosine above is very important)
sin2A=2sinA*cosA
3) Half-angle just remember this:
Tan(A/2)=( 1-cosA)/ Sina = Sina /( 1+cosA)
(4) The power reduction formula can be derived from the cosine of double angle.
(sinA)^2=( 1-cos2A)/2
(cosA)^2=( 1+cos2A)/2
5) Using the above power reduction formula, the following commonly used simplified formulas can be derived.
1-cosA=sin^(A/2)*2
1-sinA=cos^(A/2)*2