sin(-a)=-sin(a)cos(-a)= cos(a)sin(pi/2-a)= cos(a)cos(pi/2-a)= sin(a)
sin(pi/2+a)= cos(a)cos(pi/2+a)=-sin(a)sin(pi-a)= sin(a)cos(pi-a)=-cos(a)
sin(pi+a)=-sin(a)cos(pi+a)=-cos(a)tgA = tanA = sinA/cosA
2. The trigonometric function of the sum and difference of two angles
sin(a+b)= sin(a)cos(b)+cos(α)sin(b)cos(a+b)= cos(a)cos(b)-sin(a)sin(b)= sin(a)cos(b)-cos(a)sin(b)= cos(a)cos(a)cos(b)= cos(a)cos(b)+sin(a)sin(b)
tan(a+b)=(tan(a)+tan(b))/( 1-tan(a)tan(b))tan(a-b)=(tan(a)-tan(b))/( 1+tan(a)tan(b))
3, trigonometric function and differential product formula
sin(a)+sin(b)= 2 sin((a+b)/2)cos((a-b)/2)sin(a)？ sin(b)= 2cos((a+b)/2)sin((a-b)/2)
cos(a)+cos(b)= 2cos((a+b)/2)cos((a-b)/2)cos(a)-cos(b)=-2 sin((a+b)/2)sin((a-b)/2)
4, product and difference formula
sin(a)sin(b)=- 1/2 *[cos(a+b)-cos(a-b)]cos(a)cos(b)= 1/2 *[cos(a+b)+cos(a-b)]
sin(a)cos(b)= 1/2 *[sin(a+b)+sin(a-b)]
5, double angle formula
sin(2a)= 2 sin(a)cos(a)cos(2a)=cos^2(a)-sin^2(a)=2cos^2(a)- 1= 1-2sin^2(a)
6. The solution of a quadratic equation-b+√ (B2-4ac)/2a-b-b+√ (B2-4ac)/2a
The relationship between root and coefficient x1+x2 =-b/ax1* x2 = c/a Note: Vieta theorem.
Discriminant b2-4a=0 Note: The equation has two equal real roots.
B2-4ac >0 Note: The equation has real roots.
B2-4ac & lt； 0 Note: The equation has multiple yokes.
7 The first n terms of some sequences are1+2+3+4+5+6+7+8+9+…+n = n (n+1)/21+3+5+7+9+1.
2+4+6+8+ 10+ 12+ 14+…+(2n)= n(n+ 1) 12+22+32+42+52+62+72+82+…+N2 = n(n+ 1)(2n+ 1)/6
13+23+33+43+53+63+…n3 = N2(n+ 1)2/4 1 * 2+2 * 3+3 * 4+4 * 5+5 * 6+6 * 7+…+n(n+ 1)= n(n+ 1)(n+2)/3
8. Sine Theorem a/sinA=b/sinB=c/sinC=2R Note: where R represents the radius of the circumscribed circle of a triangle.
9. Cosine Theorem b2=a2+c2-2accosB Note: Angle B is the included angle between side A and side C..
10, straight prism lateral area S=c*h, oblique prism lateral area s = c' * h.
1 1, lateral area of a regular pyramid S= 1/2c*h' lateral area of a regular prism S= 1/2(c+c')h'
12, frustum side area S = 1/2(c+c')l = pi(R+R)l surface area S=4pi*r2.
13, cylindrical lateral area S=c*h=2pi*h, conical lateral area s =1/2 * c * l = pi * r * l.
14, the arc length formula l=a*r a is the radian number R >； of the central angle; 0 sector area formula s= 1/2*l*r
15, cone volume formula V= 1/3*S*H cone volume formula V= 1/3*pi*r2h.
16. volume of oblique prism V=S'L note: where s' is the area of straight section and l is the length of side.
17, cylinder volume formula; V=s*h cylinder V=pi*r2h
18, half-angle formula
sin^2(a/2)=( 1-cos(a))/2
cos^2(a/2)=( 1+cos(a))/2
tan(a/2)=( 1-cos(a))/sin(a)= sin(a)/( 1+cos(a))
General formula of trigonometric function
sin(a)=(2tan(a/2))/( 1+tan^2(a/2))
cos(a)=( 1-tan^2(a/2))/( 1+tan^2(a/2))
Tan (1) = (1)
Other formulas
A * sin (a)+b * cos (a) = sqrt (a2+B2) sin (a+c) [where tan(c)=b/a]
A * sin (a)-b * cos (a) = sqrt (a2+B2) cos (a-c) [where tan(c)=a/b]
1+sin(a)=(sin(a/2)+cos(a/2))^2
1-sin(a)=(sin(a/2)-cos(a/2))^2
Other non-critical trigonometric functions
csc(a)= 1/sin(a)
Seconds (a)= 1/ cosine (a)
Hyperbolic function
sinh(a)=(e^a-e^(-a))/2
cosh(a)=(e^a+e^(-a))/2
tgh(a)=sinh(a)/cosh(a)