Parabola: y
=
cut down on
*+
Bronx (Bronx)
+
c
Y equals ax
Square plus sign
Bx plus
c
a
& gt
When it is 0, the opening is upward.
a
& lt
When it is 0, the opening is downward.
c
=
When the value is 0, the parabola passes through the origin.
b
=
0, the parabolic axis of symmetry is the y axis.
And vertex Y.
=
a(x+h)*
+
k
That is, y equals a times the square of (x+h)+K.
-h is x of vertex coordinates.
K is y of vertex coordinates.
Generally used to find the maximum and minimum.
Parabolic standard equation: y 2 = 2px
It means that the focus of the parabola is on the positive semi-axis of X, and the focal coordinate is (p/2,0).
The alignment equation is x=-p/2.
Since the focus of a parabola can be on any semi-axis, * * has a standard equation y 2 = 2px.
y^2=-2px
x^2=2py
x^2=-2py
Trigonometric function:
Two-angle sum 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-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
tan2A=2tanA/( 1-tan2A)
cot2A=(cot2A- 1)/2cota
cos2a = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin2a
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
sin^2(α)+sin^2(α-2π/3)+sin^2(α+2π/3)=3/2
tanAtanBtan(A+B)+tanA+tan B- tan(A+B)= 0
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)]
half-angle 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))
Sum 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 = 2 sin((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