美国高中数学

:
r"
-:Jii; 6 i' -rr"'r;":tih-''t
" " ')""""':'"""+"'"""""""}'-""':'1:"
;
i ll,l2 i
.l
ln
__ i
-/l
i
i-l/y3
sino-+ 6 csc
sinz8* cos'o= I
'j cci'' ti
-l*
sec v
; ' r /it' " il | Ln
cosZr*2coszt*1
tan(x'* y) "' tan(-r* y) =,
tirnr + tang
1 * tanrtany
j,'1:-1v
I * tanxtany
Half-Angle Identities [:;;'; .r $ n ; = a\i --.-,,_".1 I Y cc)s = t V - * T - f
x i;;;;;
cos 2x = I '-' 2sln2x ?tanr ^ tan A' = ;-_:--;1 * tan'.t
x r-cosr tan; = --::--_ 2. einx
tanz=f1;;;
x
sin r
offi YdLer- risarumegisiusstistrs;
f)
t,
. ,....'..'-
Addition arld Subtraction Identities sin(r + Y) = sin r cosV -t' cos r sr.n y sin(r - A) : s i n r c o s y - c o s x s i r , y cos(x+ Y) : c(rs.r cos y - sin r sin 3l * cos(x U)= cos.xcosy + sin x sin y Double Angle Identi ties s i n 2 r= 2 s i n r c o s . r cos2; = ,:os2f sinsr
,I
()
---.i.'..
: vilz :' iiii'::
,ll,/3:
.-.-.".".. '1. "" "r"'
,ltt2 I i tn i .-. .... . ' ;....-,.-^." ll'/2 : "'t:n""'i I "
I ttL i
rr-1"'"':"""{.'"r'
I
:
,/j
1.
'=' \'? Rectangular to Polar: r
$=
Arctanl + nwhen'r<0
Polar Form of Line: P Polar Form of Conic: '
= r cos iS ._ &) : , *T;;
* Y sin 6 P=A tlormal Form of Line: r c066 sirr fl) 'r * -vi ''= r (cos t) + i Polar Form of CornplexNurnber;
- cor o
.B Stn6 e
x
of [.aw Sines: #o , s 2 + b l - Zbc cos A, t" = a2 'r c? ?'ac az * bz * ct Law of Coeines:
*e
=
;;T
-lobcosC
Area of Triang rct f,tcsin A ' A sin 1 ., j*.---.", B Zr{ sin s i nC 2" 1ffi-=;6:66
:"
"-1' tarr E
t e n O= ; i l
1*
sin I
,= SeCz0 tanr tl + 1
cot2$ = ssq?t)
i cosct sin F sin (a : P) = sin a cosP
= cos0cosB;sinasinF cos ((I, = F )
si n ?0 : : ? s i n 0 c o s 0
12
S'r)l t r t* I
= rn(cos o + i s ' i n n 0 ) rt [r(cos0 + i sin 0)Jn _r + rv' (c"u(E \r^ L"{esgtr,s'rhsJ*;
,t - +rs\o ; "'"('?--,-*l$' o )
| ,2
,'-'
loi'
xiu C'
i'o'' s i n B
l-t 9.:ti-gn 9. stn A i" :T
t L,
!,\.Lula La, B
sin + 1r + r.')
where s :: -I (' 4
* lol o Area of Circular Ssctor: A
A
= i I t.a -- sin cr) Area of Circular Sogrnent:S z Polar to Rectangular: r = rcoe0,Y * rsin0 " Z when 'r )' o' ,1, B * Arct'an
Reciprocal Identities
SeCf
['J,thagorean IrJentities
+' si-ir2.r rosli. * = 1 'l +-tan2: = secZr
NegativeAngle ldentities * sin("--r) '-sin,'{
cos(-x) = cls r tan(-r) .:" -tan r
'5 cos.r
Cofunction ldenti ties lrr \ cosr * ' t ( ; sin.r = cos[1 - x) lr \ tanr * cotit * x) cotr
-,
=
li€C f
.= fi(lt
.l
=.u.(f -secr
t
*,*(f ') csci*'*(f ,
ra'(n= o)=ffi
tan28=t:GtT
2tan0
0 - ein?I cos 110., co82 :i 12sin20
, =Z c o g l o - I
l1 +' ccs I I *.--' + cOS '; - r / i 2 1 Y ,/t 0 tunl = -Vl + cos8
+i #_
1t cosr sin r.
CO8f.
CS6I '*: *
srnr
sr"nr
tan jE =.4
.
cosr
COtX
11. COIX = --tan r
tanr:
--
cot r
1 + cot2r * csCx
Periodicity Identiti es
sin(r +2rr) = sinl c s c ( x+ 2 n ) = c s c x tan(r + rr),r tan r cos(x+ 2n) s e c ( r+ 2 n ' ) cot(;r+ n)
* isin(f}t * oill * 0t) = 1 1 r 2 { c o s ( 0 1 B n ) 02 sin 0r) ' rz(cos + i sin 0i r1(cos + f
01 r2(coE + i sin 02)
.rf:fLj:3lgil
=. 1, i6os(01 0 z ) - i s r n i O r