Home > Article > Computer Tutorials > A collection of trigonometric function calculation formulas for junior high schools: learn about them one by one
Sine function sin(A)=a/h
Cosine function cos(A)=b/h
tangent function tan(A)=a/b
Cotangent function cot(A)=b/a
Two angles and 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-tanAtanB)
tan(A-B)=(tanA-tanB)/(1 tanAtanB)
cot(A B)=(cotAcotB-1)/(cotB cotA)
cot(A-B)=(cotAcotB 1)/(cotB-cotA)
Double angle formula
tan2A=2tanA/[1-(tanA)^2]
cos2a=(cosa)^2-(sina)^2=2(cosa)^2 -1=1-2(sina)^2
sin2A=2sinA*cosA
Triple angle formula
sin3a=3sina-4(sina)^3
cos3a=4(cosa)^3-3cosa
tan3a=tana*tan(π/3 a)*tan(π/3-a)
Half-width formula
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))
cot(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
2sinAcosB=sin(A B) sin(A-B)
2cosAsinB=sin(A B)-sin(A-B) )
2cosAcosB=cos(A B) cos(A-B)
-2sinAsinB=cos(A B)-cos(A-B)
sinA sinB=2sin((A B)/2)cos((A-B)/2
cosA cosB=2cos((A B)/2)sin((A-B)/2)
tanA tanB=sin(A B)/cosAcosB
Integration 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)]
Induction formula
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
Universal formula
sin(a)= (2tan(a/2))/(1 tan^2(a/2))
cos(a)= (1-tan^2(a/2))/(1 tan^2(a/2))
tan(a)= (2tan(a/2))/(1-tan^2(a/2))
Trigonometric functions:
1. Two angles and 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-tanAtanB)
tan(A-B)=(tanA-tanB)/(1 tanAtanB)
cot(A B)=(cotAcotB-1)/(cotB cotA)
cot(A-B)=(cotAcotB 1)/(cotB-cotA)
2. Double angle formula
tan2A=2tanA/(1-tan2A) cot2A=(cot2A-1)/2cota
cos2a=cos2a-sin2a=2cos2a-1=1-2sin2a
sinα sin(α 2π/n) sin(α 2π*2/n) sin(α 2π*3/n) …… sin[α 2π*(n-1)/n]=0
cosα cos(α 2π/n) cos(α 2π*2/n) cos(α 2π*3/n) …… cos[α 2π*(n-1)/n]=0
And sin2 (α) sin2 (α-2π/3) sin2 (α 2π/3)=3/2
tanAtanBtan(A B) tanA tanB-tan(A B)=0
3.·Universal formula:
sinα=2tan(α/2)/[1 tan^2(α/2)]
cosα=[1-tan^2(α/2)]/[1 tan^2(α/2)]
tanα=2tan(α/2)/[1-tan^2(α/2)]
4. Half-width formula
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))
cot(A/2)=√((1 cosA)/((1-cosA)) cot(A/2)=-√((1 cosA)/((1-cosA))
5. Sum and difference product
2sinAcosB=sin(A B) sin(A-B) 2cosAsinB=sin(A B)-sin(A-B)
2cosAcosB=cos(A B)-sin(A-B) -2sinAsinB=cos(A B)-cos(A-B)
sinA sinB=2sin((A B)/2)cos((A-B)/2 cosA cosB=2cos((A B)/2)sin((A-B)/2)
tanA tanB=sin(A B)/cosAcosB tanA-tanB=sin(A-B)/cosAcosB
cotA cotBsin(A B)/sinAsinB -cotA cotBsin(A B)/sinAsinB
Commonly used mathematical functions
The C language system provides more than 400 standard functions (called library functions), which can be used directly when designing programs.
Library functions mainly include mathematical functions, character processing functions, type conversion functions, file management functions and memory management
Functions and other categories. Commonly used mathematical functions are described below, and other types of functions will be explained in subsequent chapters.
1. Function name: abs
Prototype: int abs(int i);
Function: Absolute value of integer.
For example, suppose x=abs(5), y=abs(–5), z=abs(0), then x=5, y=5, z=0.
2. Function name: labs
Prototype: long labs(long n);
Function: Absolute value of long integer.
For example, suppose x=labs(40000L), y=labs(–5), z=labs(0), then x=40000, y=5, z=0.
3. Function name: fabs
Prototype: double fabs(double x);
Function: Absolute value of real number.
For example, suppose x=fabs(5.3), y=fabs(–5.3), z=fabs(0), then x=5.3, y=5.3, z=0.
4. Function name: floor
Prototype: double floor(double x);
Function: The largest integer not greater than x, which is equivalent to the mathematical function [x].
For example, let x=floor(–5.1), y=floor(5.9),z=floor(5), then x= –6,y=5,z=5.
5. Function name: ceil
Prototype: double ceil(double x);
Function: The smallest integer not less than x.
For example, suppose x=ceil(–5.9), y=ceil(5.1),z=ceil(5), then x = –5,y=6,z=5
6. Function name: sqrt
Prototype: double sqrt(double x);
Function: square root of x.
For example, assuming x=sqrt(4), y=sqrt(16), then x=1.414214, y=4.0
7. Function name: log10
Prototype: double log10(double x);
Function: Common logarithm of x.
8. Function name: log
Prototype: double log(double x);
Function: natural logarithm of x.
9. Function name: exp
Prototype: double exp(double x);
Function: Euler’s constant e raised to the x power.
10. Function name: pow10
Prototype: double pow10(int p);
Function: 10 to the pth power.
For example, let x=pow10(3),y=pow10(0), then x=1000,y=1
11. Function name: pow
Prototype: double pow(double x, double y);
Function: x to the yth power.
For example, if x=pow(3,2),y=pow(–3,2), then x=9,y=9
12. Function name: sin
Prototype: double sin(double x);
Function: Sine function.
13. Function name: cos
Prototype: double cos(double x);
Function: Cosine function.
14. Function name: tan
Prototype: double tan(double x);
Function: Tangent function.
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