I. formulas of trigonometric functions
1, sum of two angles formula
sin(A+B)= Sina cosb+cosAsinBsin(A-B)= Sina cosb-sinBcosA
cos(A+B)= cosa cosb-Sina sinb cos(A-B)= cosa cosb+Sina sinb
tan(A+B)=(tanA+tanB)/( 1-tanA tanB)tan(A-B)=(tanA-tanB)/( 1+tanA tanB)
2. Double angle formula
tan2A = 2 tana/( 1-tan2A)ctg2A =(ctg2A- 1)/2c TGA
cos2a = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin2a
Second, the area formula:
Side area of right-angle prism S=c*h
Side area of oblique prism s = c' * h
The side area of a regular pyramid is S= 1/2c*h'
The side area of the prism is s = 1/2(c+c')h'
The lateral area of the frustum of a cone is s =1/2 (c+c') l = pi (r+r) l.
The surface area of the ball S=4pi*r2.
The lateral area of the cylinder is s = c * h = 2pi * h
The lateral area of the cone is s =1/2 * c * l = pi * r * l.
Third, the commonly used formula of factorization.
1, square difference formula: a? -B? =(a+b)(a-b)
2. Complete square formula: a? +2ab+b? =(a+b)?
3. Cubes and formulas: A? +b? =(a+b)(a? -ab+b? )
4. Cubic difference formula: a? -B? =(a-b)(a? +ab+b? )
5. Complete cubes and formulas: a? +3a? b+3ab? +b? =(a+b)?
6. Complete cubic difference formula: a? -3a? b+3ab? -B? =(a-b)?
7. Three complete square formulas: A? +b? +c? +2ab+2bc+2ac=(a+b+c)?
8. Three cubes and formulas: A? +b? +c? -3abc=(a+b+c)(a? +b? +c? -ab-bc-ac)
Four, the area formula of common graphics
Area of rectangle = length× width S=ab
Area of a square = side length × side length S=a?
Area of triangle = base × height ÷2S=ah÷2
Area of parallelogram = base × height S=ah
Trapezoidal area = (upper bottom+lower bottom) × height ÷2S=(a+b)h÷2.
Area of circle = π× radius× radius
Five, perimeter formula
Circle: C=πd=2πr (d is diameter, r is radius, π).
The circumference of a triangle is C = a+b+c(abc is three sides of a triangle).
Quadrilateral: C=a+b+c+d(abcd is the side length of quadrilateral)
Rectangle: C=2(a+b) (a is long and b is wide)
Square: C=4a(a is the side length of the square)
Polygon: C= sum of all sides.
Sector circumference: C = 2R+nπR÷ 180? (n= central angle) = 2R+kR (k= radian)