1. unit vector: unit vector a0= vector a/| vector a|

2.P(x, y) then vector OP=x vector i+y vector j.

| vector OP|= root sign (x square +y square)

3.P2(x2，y2)

Then the vector p 1p2 = {x2-x 1, y2-y 1}

| vector P 1P2|= radical sign [(x2-x 1) square +(y2-y 1) square]

4. Vector A = {x 1, x2} Vector B = {x2, y2}

Vector a* vector b=| vector a | | vector b | * cos α = x1x2+y1y2.

Cosα= vector a* vector b/| vector a|*| vector b|

(x 1x2+y 1y2)

= ————————————————————

Root number (x 1 square +y 1 square) * root number (x2 square +y2 square)

5. Space vector: same as above.

(Hint: Vector A = {x, y, z})

6. Necessary and sufficient conditions:

If vector a⊥ vector b

Then vector a* vector b=0

If vector a// vector b

Then vector a* vector b =+| vector a|*| vector b= |

Or x 1/x2=y 1/y2.

7. Vector A Vector b| Square

= | Vector a| Square+| Vector b| Square 2 Vector a* Vector B.

= (Vector A, Vector B) squared

Formulas of trigonometric functions:

1. General formula

Let tan(a/2)=t

sina=2t/( 1+t^2)

cosa=( 1-t^2)/( 1+t^2)

tana=2t/( 1-t^2)

2. Auxiliary angle formula

asint+bcost=(a^2+b^2)^( 1/2)sin(t+r)

cosr=a/[(a^2+b^2)^( 1/2)]

sinr=b/[(a^2+b^2)^( 1/2)]

tanr=b/a

3. Triple angle formula

sin(3a)=3sina-4(sina)^3

cos(3a)=4(cosa)^3-3cosa

tan(3a)=[3tana-(tana)^3]/[ 1-3(tana^2)]

4. Sum and difference of products

Sina * cosb =[sin(a+b)+sin(a-b)]/2

cosa * sinb =[sin(a+b)-sin(a-b)]/2

cosa * cosb =[cos(a+b)+cos(a-b)]/2

Sina * sinb =-[cos(a+b)-cos(a-b)]/2

5. Sum and difference of products

Sina+sinb = 2 sin[(a+b)/2]cos[(a-b)/2]

Sina-sinb = 2sin[(a-b)/2]cos[(a+b)/2]

cosa+cosb = 2cos[(a+b)/2]cos[(a-b)/2]

cosa-cosb =-2 sin[(a+b)/2]sin[(a-b)/2]