Formulas of trigonometric functions, senior high school all function formulas.
Two-angle sum formula
sin(A+B) = sinAcosB+cosAsinB
sin(A-B) = sinAcosB-cosAsinB
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)
cot(A+B)=(cotA cotB- 1)/(cot B+cotA)
cot(A-B)=(cotA cotB+ 1)/(cot b-cotA)
Double angle formula
2tanA/( 1-tan^2 A)
Sin2A=2SinA？ Kosa
Cos2A = Cos^2 A - Sin^2 A
=2Cos^2 A— 1
= 1—2sin^2 A
Triple angle formula
sin3a = 3sina-4(sina)^3；
cos3A = 4(cosA)^3 -3cosA
tan3a = tan a？ tan(π/3+a)？ tan(π/3-a)
half-angle formula
sin(A/2) = √{( 1 - cosA)/2}
cos(A/2) = √{( 1+cosA)/2}
tan(A/2)= √{( 1-cosA)/( 1+cosA)}
cot(A/2)= √{( 1+cosA)/( 1-cosA)}
Tan(A/2)=( 1-cosA)/ Sina = Sina /( 1+cosA)
Sum difference product
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]
tanA+tanB=sin(A+B)/cosAcosB
Sum and difference of products
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)]
cos(a)sin(b)= 1/2 *[sin(a+b)-sin(a-b)]
Inductive formula
sin(-a) = -sin(a)
cos(-a) = cos(a)
sin(π/2-a) = cos(a)
cos(π/2-a) = sin(a)
sin(π/2+a) = cos(a)
cos(π/2+a) = -sin(a)
sin(π-a) = sin(a)
cos(π-a) = -cos(a)
sin(π+a) = -sin(a)
cos(π+a) = -cos(a)
tgA=tanA = sinA/cosA
General formula of trigonometric function
sin(a)=[2tan(a/2)]/{ 1+[tan(a/2)]^2}
cos(a)= { 1-[tan(a/2)]^2}/{ 1+[tan(a/2)]^2}
Tan (1) = [2 tan (a/2)]/{1-[tan (a/2)] 2}
Other formulas
Answer? Sin (a)+b? Cos(a)=[√( a2+B2)]* sin(a+c)[ where tan(c)=b/a]
Answer? Crime (A)-B? Cos(a)=[√( 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
tg h(a) = sin h(a)/cos h(a)
How to learn functions is the easiest. The function of junior high school will be simpler. Mainly linear function and quadratic function.
The content of linear function is generally simple, and the skill of solving problems is mainly to set the resolution function, and then find out the corresponding conditions according to the setting.
It is suggested to preview in advance, and then remember clearly that y=kx+b(k is not equal to 0) is in k>0, b>0; k & gt0，b & lt0; k & lt0，b & gt0; Images of k<0 and b<0.
Quadratic function will be more difficult. Y = ax 2+bx+c (a is not equal to 0)
It is suggested to start with the image and pay attention to a>0 and A.
According to the needs of the topic, flexibly choose the solutions of vertex Y = A (X-M) 2+N, two points y=a(x-x 1)(x-x2) and general Y = AX 2+BX+C.
Function function, naturally, is the most important image, and the big questions are basically the big synthesis of function+geometry.