SAT II数学Level IIC常用公式总结pdf版

If 2.
z1 r1 [cos(1 2 ) i sin(1 2 )] z2 r2
3.z n r n (cos n 2 i sin n 2 ) r n cisn 4.z1/ n r1/ n (cos
2 k
n n n where k is an integer taking on values from 0 to n-1.
2
If B 4 AC 0 , the graph is a hyperbola.
2
Circle:
( x h) 2 ( y k ) 2 r 2
Ellipse:
( x h) 2 ( y k ) 2 if C>A, 1 , transverse axis horizontal a2 b2
y A f ( Bx C ) A is the amplitude f is the period of the graph B C is the phase shift B
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*The correct sign for Formulas 15 through 17is determined by the quadrant in which angle Triangles Law of sines:
1 A lies. 2
sin A sin B sin C a b c

3
or 60
2 2 2 2
1
3 2
cosine
3 2 3 3
3
1 2
3
tangent
cotangent
1
3 2
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2 3 3
2
2
cosecant
2
2 3 3
MATH LEVEL IIC
1.3ver
CHAPTER 1 INTRODUCTION TO FUNCTIONS (f+g)(x)=f(x)+g(x) (f·g)(x)=f(x)·g(x) (f/g)(x)=f(x)/g(x) (f g)(x)=f(x) g(x)=f(g(x)) CHAPTER 2 POLYNOMIAL FUNCTIONS Linear Functions Distance= (x1 -x 2 ) +(y1 -y2 ) Distance=
c =1 a
Length of latus rectum=4p Hyperbola:
( x h) 2 ( y k ) 2 1 , transverse axis horizontal a2 b2 ( y k ) 2 ( x h) 2 1 , transverse axis vertical, where c 2 a 2 b2 a2 b2
10.sin 2 A 2sin A cos A 11.cos 2 A cos 2 A sin 2 A 12.cos 2 A 2 cos 2 A 1 13.cos 2 A 1 2sin 2 A 2 tan A 14.tan 2 A 1 tan 2 A 1 1 cos A 15.sin A 2 2 1 1 cos A 16.cos A 2 2 1 1 cos A A 2 1 cos A 1 cos A 18. sin A sin A 19. 1 cos A 17.tan
a b (vertical)or (horizontal). b a
the slopes of the asymptotes are
Exponential and Logarithmic Functions
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1 Area bc sin A 2 1 Area of a : Area ac sin B 2 1 Area ab sin C 2
CHAPTER 4 MISCELLANEOUS RELATIONS AND FUNCTIONS The general quadratic equation
sin csc 1 cos sec 1 tan cot 1 sin tan cos cos cot sin
Quadrant Function: sin,csc cos,sec tan,cot Arcs and Angles I + + + II + III + IV + -
Ax 2 Bxy Cy 2 Dx Ey F 0
If B 4 AC 0 and A C , the graph is a circle.
2
If B 4 AC 0 and A C , the graph is an ellipse.
2
If B 4 AC 0 , the graph is a parabola.
Formulas:
1.sin 2 x cos 2 x 1 2.tan x 2 1 sec2 x 3.cot 2 x 1 csc 2 x 4.sin( A B) sin A cos B cos A sin B 5.sin( A B) sin A cos B cos A sin B 6.cos( A B) cos A cos B sin A sin B 7.cos( A B) cos A cos B sin A sin B tan A tan B 8.tan( A B) 1 tan A tan B tan A tan B 9.tan( A B) 1 tan A tan B
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SAT II 数学 Level IIC 常用公式

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x a x b x a b x0 1 xa x a b b x 1 xa a x a b ( x ) x ab x a y a ( xy ) a log b ( p q ) log b p log b q log b 1 0 b logb p p p log b log b p log b q q log b b 1 log b ( p x ) x log b p log b p log a p log a b
if C<A,
( x h) 2 ( y k ) 2 1 , transverse axis vertical, where a 2 b2 c 2 2 2 b a
Vertices: a units along major axis from center Foci: c units along major axis from center Length=2b Eccentricity=
s r 1 A r 2 2
Special Angles 0 sine cosine tangent cotangent secant cosecant 0 1 0 und 1 und
2
1 0 und 0 und 1

0 -1 0 und -1 und
3 2
-1 0 und 0 und -1
Vertices: a units along the transverse axis from center Foci: c units along the transverse from center Length of latus rectum=
2b 2 a
Eccentricity=
c >1 a
z1 x1 y1i r1 (cos 1 i sin 1 ) r1cis1 and z2 x2 y2i r2 (cos 2 i sin 2 ) r2cis 2 : 1.z1 z2 r1 r2 [cos(1 2 ) i sin(1 2 )]
MISCELLANEOUS TOPICS
i sin
2 k
) r1/ n cis
2 k
CHAPTER 5
n ! n(n 1)(n 2)...3 2 1
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a 2 b 2 c 2 2bc cos A
Law of cosines: b a c 2ac cos B
2 2 2
c 2 a 2 b 2 2ab cos C
c <1 a
2b 2 Length of latus rectum= a
Parabola: if C=0, ( x h) 4 p( y k ) opens up and down---axis of symmetry is vertical
2
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Greatest Integer Functions:
x i, where i is an interger and i x i 1
Polar Coordinates:
x r cos y r sin x2 y 2 r 2
De Moivre’s Throrem:
2 0 1 0 und 1 und
*und: means that the function is undefined because the definition of the function necessitates division by zero.