A collection of trigonometric function calculation formulas for junior high schools: learn about them one by one

Who can give me the complete set of trigonometric formulas for junior high school

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 function calculation formula

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

C language simply calculates trigonometric functions, four arithmetic operations, power functions, exponential functions

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.

The above is the detailed content of A collection of trigonometric function calculation formulas for junior high schools: learn about them one by one. For more information, please follow other related articles on the PHP Chinese website!