Mathematical key formula
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)
ctg(A+B)=(ctgActgB- 1)/(ctg B+ctgA)
ctg(A-B)=(ctgActgB+ 1)/(ctg b-ctgA)
sin(A/2)=√(( 1-cosA)/2)sin(A/2)=-√(( 1-cosA)/2)
cos(A/2)=√(( 1+cosA)/2)cos(A/2)=-√(( 1+cosA)/2)
tan(A/2)=√(( 1-cosA)/(( 1+cosA))
tan(A/2)=-√(( 1-cosA)/(( 1+cosA))
ctg(A/2)=√(( 1+cosA)/(( 1-cosA))
ctg(A/2)=-√(( 1+cosA)/(( 1-cosA))
similar triangles
Test center: similar triangles's concept, the meaning of similarity ratio, and the enlargement and reduction of drawing graphics.
Assessment requirements: (1) Understand the concept of similarity; (2) Grasp the characteristics of similar figures and the significance of similarity ratio, and zoom in and out known figures as required.
Test sites: the proportion theorem of parallel lines and the related theorem of parallel lines on one side of a triangle.
Examination requirements: Use the proportional theorem of parallel lines to understand and solve some geometric proofs and geometric calculations.
Note: An edge judged to be parallel cannot be used as the corresponding line segment in the condition in proportion.
Test site: similar triangles's concept
Evaluation requirements: Based on the concept of similar triangles, master the characteristics of similar triangles and understand the definition of similar triangles.
Inspection Center: similar triangles's Judgment, Nature and Application
Examination requirements: Master similar triangles's judgment theorem (including preliminary theorem, three judgment theorems, right triangle similarity judgment theorem) and its properties, and can apply it well.
Axisymmetric graphics and centrally symmetric graphics
Axisymmetric graphics: line segment, angle, isosceles triangle, equilateral triangle, diamond, rectangle, square, isosceles trapezoid and circle.
Number of symmetry axes: an angle has a symmetry axis, that is, the angle bisector of the angle; The isosceles triangle has an axis of symmetry, which is the median vertical line of the base; An equilateral triangle has three axes of symmetry, that is, the median vertical lines on three sides; A diamond has two symmetry axes, which are straight lines where two diagonals are located, and a rectangle has two symmetry axes, which are straight lines between two groups of opposite sides.
Centrally symmetric figures: line segments, parallelograms, diamonds, rectangles, squares and circles.
Symmetry center: the symmetry center of the line segment is the midpoint of the line segment; The symmetrical center of parallelogram, rhombus, rectangle and square is the intersection of diagonal lines, and the symmetrical center of circle is the center of circle.
Description: Line segments, diamonds, rectangles, squares and circles are all symmetrical figures.
The above is the key content of the notes I gave you on math study in Grade One of Senior High School, which is for reference only and I hope it will help you.