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考研数学二公式高数线代(费了好大的劲)技巧归纳(新).docx

90°-a
cosa
sina
ctga
tga
90+a
cosa
-sina
-ctga
-tga
180。-a
sina
-cosa
-tga
-ctga
180。+a
-sina
-cosa
tga
ctga
270。-a
-cosa
-sina
ctga
tga
2700+a
-cosa
sina
-ctga
-tga
360。-a
-sina
cosa
-tga
-ctga
3600+a
sina
cosa
tga
ctga

・倍角公式:

sin2
cos2
ctg2
tg2
2sincos2cos21ctg21
2ctg2tg
1tg2
12sin2
2cos
2sin
3
sin33sin4sin
3
cos34cos3cos
tg3
3tgtg3
13g2
・半角公式:
'1cossin—J
2V2
1cos1costg_
2，1cossin
sin
1cos
1coscos—.
2'2
'1cos1cossinctg—J
2V1cossin1cos
.正弦定理：2R
sinAsinBsinC
22,2

2
arctgx
arcctgx

n(n)小k(nk)(k)
(UV)CnUVk0
(n)(ni)n(n1)(n2)n(n1)(nk
uvnuvuv
2!k!

1)(nk)(k)
—uv
uv
(n)

M点的曲率：KlimI—I—।y
s01s|dsQiy2)3

1

a

b

a
b

a
f(x)
f(x)
b

a
ba,
(y。Vin
ba「1/、
GW。I)
ba\f(X)丁[(y。yn)
yn1)
yi
yn
2(V2V4
l]
Vn2)4(yiy3
yn1)]

kmm2,k为引力系数r

_____—1b

baa

b
-2
f(t)dtaa

dtu
zf[u(x,y),v(x,y)]—
x

du—dx—dydv
xy

dx

x
,uuu
du——dx——dy——dz
xyz
fx(x,y)xfy(x,y)y
uzv

tvt
zuzv

uxvx
vv
dxdy
xy
2

FydxxFyyFydx
FxzFy
Fz'yFz

u
1
(F,G)
v
1
(F,G)
x
j
(x,v)
x
j
(u,x)
u
1
(F,G)
v

(F,G)
y
J
(y,v)
y
j
(u,y)
FF

G(x,y,u,v)0(u,v)GG
uv
Fu
Gu
Fv
Gv

fy(xo,yo)0,令：fxx(xo,yo)A,
fxy(xo,yo)B,fyy(xo,yo)