Sine equals hypotenuse: sina = a/c.

Cosine (cos) is equal to the ratio of adjacent side to hypotenuse: COSA = b/c.

Tangent (tan) is equal to the opposite side than the adjacent side: tana = a/b.

Cotangent (cot) equals adjacent edge: COTA = B/A.

Sec is equal to the hypotenuse than the adjacent side: seca = c/b.

Cotangent (csc) equals the comparison of hypotenuse and edge: CSCA = C/A.

The relationship between 1 trigonometric function and complementary angle

sin(90 -α)=cosα，cos(90 -α)=sinα，

tan(90 -α)=cotα，cot(90 -α)=tanα。

2. Square relation

sin^2(α)+cos^2(α)= 1

tan^2(α)+ 1=sec^2(α)cot^2(α)+ 1=csc^2(α)

3, the relationship between products

sinα=tanα cosα

cosα=cotα sinα

tanα=sinα secα

cotα=cosα cscα

secα=tanα cscα

cscα=secα cotα

4. Reciprocal relationship

tanα cotα= 1

sinα cscα= 1

cosα secα= 1

5. Acute angle formula of trigonometric function, trigonometric function of sum and difference of two angles:

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)

6. Triangular sum of trigonometric functions:

sin(α+β+γ)= sinαcosβcosγ+cosαsinβcosγ+cosαcosβsinγ-sinαsinβsinγ

cos(α+β+γ)= cosαcosβcosγ-cosαsinβsinγ-sinαcosβsinγ-sinαsinαsinβcosγ-sinαsinβcosγ

tan(α+β+γ)=(tanα+tanβ+tanγ-tanαtanβtanγ)/( 1-tanαtanβ-tanβtanγ-tanγtanα)

7. Auxiliary angle formula:

Asinα+bcosα = (A2+B2) (1/2) sin (α+t), where

sint=B/(A^2+B^2)^( 1/2)

cost=A/(A^2+B^2)^( 1/2)

ant=B/A

asinα+bcosα=(a^2+b^2)^( 1/2)cos(α-t),tant=a/b

8. Double angle formula:

sin(2α)=2sinα cosα=2/(tanα+cotα)

cos(2α)=cos^2(α)-sin^2(α)=2cos^2(α)- 1= 1-2sin^2(α)

tan(2α)=2tanα/[ 1-tan^2(α)]

9, triple angle formula:

sin(3α)=3sinα-4sin^3(α)

cos(3α)=4cos^3(α)-3cosα

10, half-angle formula:

sin(α/2)= √(( 1-cosα)/2)

cos(α/2)= √(( 1+cosα)/2)

tan(α/2)=√(( 1-cosα)/( 1+cosα))= sinα/( 1+cosα)=( 1-cosα)/sinα

1 1, power reduction formula:

sin^2(α)=( 1-cos(2α))/2=versin(2α)/2

cos^2(α)=( 1+cos(2α))/2=covers(2α)/2

tan^2(α)=( 1-cos(2α))/( 1+cos(2α))

12, general 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)]

13, product sum and difference formula:

sinαcosβ=( 1/2)[sin(α+β)+sin(α-β)]

cosαsinβ=( 1/2)[sin(α+β)-sin(α-β)]

cosαcosβ=( 1/2)[cos(α+β)+cos(α-β)]

sinαsinβ=-( 1/2)[cos(α+β)-cos(α-β)]

14, sum-difference product formula:

sinα+sinβ= 2 sin[(α+β)/2]cos[(α-β)/2]

sinα-sinβ= 2cos[(α+β)/2]sin[(α-β)/2]

cosα+cosβ= 2cos[(α+β)/2]cos[(α-β)/2]

cosα-cosβ=-2 sin[(α+β)/2]sin[(α-β)/2]

15, deducing formula:

tanα+cotα=2/sin2α

tanα-cotα=-2cot2α

1+cos2α=2cos^2α

1-cos2α=2sin^2α

1+sinα=(sinα/2+cosα/2)^2