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PRE-CALCULUS FORMULA BOOKLET - C-pp HS learning lab site

PRE-CALCULUS FORMULA BOOKLETUNIT 1 CHAPTER 1 RELATIONS, FUNCTIONS,AND GRAPHS SLOPE: 1212xxyym SLOPE-INTERCEPT FORM OF A LINE: bmxy POINT-SLOPE FORM OF A LINE: )()(11xxmyy STANDARD FORM OF A LINE: 0 CByAx or CByAx CHAPTER 2 SYSTEMSOF LINEAREQUATIONS AND INEQUALITIES REFLECTION MATRICES 1001axisxr 1001_axisyr 0110xyr ROTATION MATRICES 011090 R 1001180 R 0110270 R DETERMINANTS 2X2: bcaddcbadcba det 3x3: 332213322133221333222111333322111detbaba ccacabcbcbacbacbacbacbacbacba CHAPTER 3 THE NATURE OF GRAPHS EVEN FUNCTIONS: );()(xfxf symmetric with respect to the y-axis ODD FUNCTIONS: );()(xfxf symmetric with respect to the origin DIRECT VARIATION: 0, nkxyn INVERSE VARIATION: 0, nxkyn JOINT VARIATION: ,nnzkxy where 0,0 zxand 0 n CHAPTER 4 POLYNOMIALS AND RATIONAL FUNCTIONS QUADRATIC FORMULA : aacbbx242 UNIT 2 CHAPTER 5 THE TRIGONOMETRIC FUNCTIONS LAW OF SINES: CcBbAasinsinsin or cCbBaAsinsinsin AREA OF A TRIANGLE CabKsin21 CBAcKsinsinsin212 Hero s FORMULA : ,))()((csbsassK where 2cbas LAW OF COSINES: Cabbaccos2222 CHAPTER 6 GRAPHS OF TRIGONOMETRIC FUNCTIONS LENGTH OF AN ARC: rs AREA

SEQUENCES AND SERIES THE nth TERM OF AN ARITHMETIC SEQUENCE an a1 (n 1)d SUM OF A FINITE ARITHMETIC SERIES ( ) 2 1n a a n S THE nth TERM OF A GEOMETRIC SEQUENCE 1 1 n an a r SUM OF A FINITE GEOMETRIC SERIES r a a r S n n 1 1 1 THEOREMS FOR LIMITS LIMIT OF A SUM n n n n n n n (a b ) alim b o f o f o f LIMIT OF A DIFFERENCE n …

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Transcription of PRE-CALCULUS FORMULA BOOKLET - C-pp HS learning lab site

1 PRE-CALCULUS FORMULA BOOKLETUNIT 1 CHAPTER 1 RELATIONS, FUNCTIONS,AND GRAPHS SLOPE: 1212xxyym SLOPE-INTERCEPT FORM OF A LINE: bmxy POINT-SLOPE FORM OF A LINE: )()(11xxmyy STANDARD FORM OF A LINE: 0 CByAx or CByAx CHAPTER 2 SYSTEMSOF LINEAREQUATIONS AND INEQUALITIES REFLECTION MATRICES 1001axisxr 1001_axisyr 0110xyr ROTATION MATRICES 011090 R 1001180 R 0110270 R DETERMINANTS 2X2: bcaddcbadcba det 3x3: 332213322133221333222111333322111detbaba ccacabcbcbacbacbacbacbacbacba CHAPTER 3 THE NATURE OF GRAPHS EVEN FUNCTIONS: );()(xfxf symmetric with respect to the y-axis ODD FUNCTIONS: );()(xfxf symmetric with respect to the origin DIRECT VARIATION: 0, nkxyn INVERSE VARIATION: 0, nxkyn JOINT VARIATION: ,nnzkxy where 0,0 zxand 0 n CHAPTER 4 POLYNOMIALS AND RATIONAL FUNCTIONS QUADRATIC FORMULA : aacbbx242 UNIT 2 CHAPTER 5 THE TRIGONOMETRIC FUNCTIONS LAW OF SINES: CcBbAasinsinsin or cCbBaAsinsinsin AREA OF A TRIANGLE CabKsin21 CBAcKsinsinsin212 Hero s FORMULA : ,))()((csbsassK where 2cbas LAW OF COSINES: Cabbaccos2222 CHAPTER 6 GRAPHS OF TRIGONOMETRIC FUNCTIONS LENGTH OF AN ARC: rs AREA OF A CIRCULAR SECTOR: 221rA ANGULAR VELOCITY: t LINEAR VELOCITY: trv CHAPTER 7 TRIGONOMETRIC IDENTITIES AND EQUATIONS PYTHAGOREAN IDENTITIES: 222222csccot1sec1tan1cossin SUM AND DIFFERENCE IDENTITIES.

2 Tantan1tantan)tan(sincoscossin)sin(sinsi ncoscos)cos( DOUBLE-ANGLE IDENTITIES: 22222tan1tan22tansin212cos1cos22cossinco s2coscossin22sin CHAPTER 7 CONTINUED HALF-ANGLE IDENTITES: 1cos,cos1cos12tan2cos12cos2cos12sin NORMAL FORM OF A LINEAR EQUATION: 0sincos pyx DISTANCE FROM A POINT TO A LINE: 2211 BACByAxd CHAPTER 8 VECTORS AND PARAMETRIC EQUATIONS VECTORS IN A PLANE (2-D) 21,aaa and 21,bbb INNER (DOT) PRODUCT: 2211bababa VECTORS IN SPACE (3-D) 321,,aaaa and 321,,bbbb INNER (DOT) PRODUCT: 332211babababa CROSS PRODUCT: kbbaajbbaaibbaaba 212131313232 PARAMETRIC EQUATIONS FOR THE PATH OF A PROJECTILE 221sincosgtvtyvtx UNIT 3 CHAPTER 9 POLAR COORDINATES AND COMPLEX NUMBERS MULTIPLE REPRESENTATIONS OF ).,( r )2,(kr or ))12(,( kr DISTANCE FORMULA IN POLAR PLANE If ),(111 rP and ),(222 rP, then )cos(21221222121 rrrrPP CONVERTING POLAR TO RECTANGULAR ),(),(yxr sincosryrx RECTANGULAR TO POLAR ),(),( ryx 22yxr xy1tan , when 0 x xy1tan, when 0 x POLAR FORM OF A LINEAR EQUATION )cos( rp POLAR FORM OF A COMPLEX NUMBER )sin(cos ir PRODUCT OF A COMPLEX NUMBER IN POLAR FORM ))sin()(cos()sin(cos)sin(cos212121222111 irririr QUOTIENT OF A COMPLEX NUMBER IN POLAR FORM )]sin()[cos()sin(cos)sin(cos212121222111 irririr De MOIVRE S THEOREM )sin(cos)]sin(cos[ ninrirnn THE p DISTINCT pth ROOTS OF A COMPLEX NUMBER )2sin2(cos)]sin(cos[11pnipnrirpp where n = 0, 1, 2, 3.

3 , p 1 CHAPTER 10 INTRODUCTION TO ANALYTIC GEOMETRY DISTANCE FORMULA FOR TWO POINTS 212212)()(yyxxd MIDPOINT OF A LINE SEGMENT )2,2(2121yyxxmidpt STANDARD FORM OF THE EQUATION OF A CIRCLE 222)()(rkyhx GENERAL FORM OF THE EQUATION OF A CIRCLE 022 FEyDxyx, where D, E and F are constants STANDARD FORM OF THE EQUATION OF AN ELLIPSE 1)()(2222 bkyahx or 1)()(2222 bhxaky where 222bac GENERAL FORM OF THE EQUATION OF AN ELLIPSE 022 FEyDxCyAx, where 0 Aand 0 C and A and C have the same signs. STANDARD FORM OF THE EQUATION OF A HYPERBOLA Form 1:1)()(2222 bkyahx or Form 2: 1)()(2222 bhxaky where 222cba EQUATIONS OF THE ASYMPTOTES OF A HYPERBOLA Form 1:)(hxabky or Form 2: )(hxbaky RECTANGULAR HYPERBOLA cxy where c is a nonzero constant GENERAL FORM OF THE EQUATION OF A HYPERBOLA 022 FEyDxCyAx where 0,0 CAand A and C have different signs.

4 CHAPTER 10 CONTINUED STANDARD FORM OF THE EQUATION OF A PARABOLA )(4)(2hxpky or )(4)(2kyphx GENERAL FORM OF THE EQUATION OF A PARABOLA 02 FEyDxy when the directrix is parallel to the y-axis 02 FEyDxx when the directrix is parallel to the x-axis GENERAL EQUATION FOR CONIC SECTIONS 022 FEyDxCyBxyAx where A, B and C are not all zero CHAPTER 11 EXPONENTIAL AND LOGARITHMIC FUNCTIONS DEFINITION OF nb1 nnbb 1 RATIONAL EXPONENTS mnnmnmbbb)( NEGATIVE EXPONENTS nnbb1 EXPONENTIAL GROWTH OR DECAY IN TERMS OF e trNN)1(0 kteNN0 COMPOUND INTEREST CONTINUOUS COMPOUNDED INTEREST ntnrPtA 1)( rtPetA )( LOGARITHMIC FUNCTIONS xbxyyb log CHAPTER 11 CONTINUED LOGARITHMIC PROPERTIES (work for both log and ln) nmnmmpmnmnmnmmnbbbpbbbbbbb loglogloglogloglogloglogloglog CHANGE OF BASE FORMULA annbbalogloglog CHAPTER 12 SEQUENCES AND SERIES THE nth TERM OF AN ARITHMETIC sequence dnaan)1(1 SUM OF A FINITE ARITHMETIC SERIES )(21nnaanS THE nth TERM OF A geometric sequence 11 nnraa SUM OF A FINITE geometric SERIES rraaSnn 111 THEOREMS FOR LIMITS LIMIT OF A SUM nnnnnnnbabalimlimlim)( LIMIT OF A DIFFERENCE nnnnnnnbabalimlimlim)( LIMIT OF A PRODUCT nnnnnnnbabalimlimlim CHAPTER 12 CONTINUED LIMIT OF A QUOTIENT nnnnnnnbabalimlimlim , where 0lim nnb LIMIT OF A CONSTANT ccnn lim, where ccn for each n SUM OF AN INFINITE geometric SERIES raS 11, when 1 r n FACTORIAL 123)3)(2)(1(!

5 Nnnnn BINOMIAL THEOREM nnnnnnnnnnnnnrrrnrnyxCyxCyxCyxCyxCyxC011 1222111000 EXPONENTIAL SERIES !5!4!3!21!54320xxxxxnxennx TRIGONOMETRIC SERIES !9!7!5!3)!12()1(sin!8!6!4!21)!2()1(cos97 53012864202xxxxxnxxxxxxnxxnnnnnn EULER S FORMULA sincosiei


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