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by: Asif Khan

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# Final Exam Study Guide Math 163

Marketplace > Old Dominion University > Math > Math 163 > Final Exam Study Guide
Asif Khan
ODU
Precalculus II
Robert Williams

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I have taken all the math notes I typed on my computer and combined them into THIS!
COURSE
Precalculus II
PROF.
Robert Williams
TYPE
Study Guide
PAGES
7
WORDS
KARMA
50 ?

## Popular in Math

This 7 page Study Guide was uploaded by Asif Khan on Wednesday December 2, 2015. The Study Guide belongs to Math 163 at Old Dominion University taught by Robert Williams in Summer 2015. Since its upload, it has received 67 views. For similar materials see Precalculus II in Math at Old Dominion University.

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Date Created: 12/02/15
Chapter 6 Study Guide 6 1 Verifying Trig Identities Identities You Need To Know RECIPROCAL IDENTITIES QUOTIENT IDENTITIES l 39 A s1nx D secx G tanxz smx csc x cosx cosx 1 1 B cosx E cscx H cotxch x sec x 5m x 5m x C tan 1 F cot x cot x tan x PYTHAGOREAN IDENTITIES 2 A sinzx coszx 1 or B 1 tan2x seczx C 1 cotzx csc x 2 coszx 1 sin x or sinzx 1 coszx Examples secA2X1tanxtanx cscxsinXcosxcotx 62 Sum and Difference Formulas HifIliLa Aquot Iiquot Fi T1 1 mm ET ff mmng mmgm ff Lme mm ffT PEI1fo 512m f2 am 1 15nr1ff Lama 3 I T Ei391f am 33 Examples Cos pi 12 Cos 7pi 12 Sin 5pi12 Tan 5pi 12 63 Double and HalfAngle Formulas Double Angle Formulas 5111 2x 2 sm xcos x COS 2x COS x Sin x J 2 tan x 2008 26 1 tan 2x q I 3 l tan x l 231n x Half Angle Formulas x l cosx x lcosx sm 2 i 008 i 2 2 2 2 x l COS 6 sin x The or depends in taH which quadrant the original 5111 x 1 COS X given value exists Cos theta45 theta is in Q1 Sin 2theta Cos 2theta Tan 2theta Cos theta35 theta is in QIV Sin theta2 Cos theta2 Tan theta2 71 Law of Sines Law of Sines gt Used when you know the measure of an angle and the length of its corresponding side sinA sinB sinC a b c mooo swausmomneurmm sinA sinB sinC 72 Law of Cosines Law of Cosines gt Used when you know the measure of an angle or the length of its corresponding side 0 In this situation Law of Sines cannot be used gt Law of Sines can be used after using Law of Cosines Law of Cosines a2 b2 6 mac cosA b2 a2 c2 Zac 2058 c2 32 b2 Zabo cosc 2 m matrwaeehouso can 74 Vectors A vector is a quantity that has direction and magnitude Magnitude of a Vector Magnitude of VIIVII If vltX ygt Vsquare root of XA2yquot2 Adding Vectors ABlta1 a2gtltb1 b2gtlta1b1 a2b2gt Unit Vector A vector with a magnitude of 1 Ult2 7gt2i7j Find Components of a Vector Using Trig Sin thetay V gty v sin theta Cos thetax V gt v cos theta 75 The Dot Product Alta1 a2gt Bltb1 b2gt ABlta1b1 a2b2gtBA ABIAIIBIcos theta If the angle between two vectors is zero vectors are parallel If UVO U and V are perpendicular or orthogonal m gt The work done by a force F to move an object from point P to Q is WFPQcos theta 77 Complex Numbers A complex number is of the form zxiy Where isquare root of l Modulus Magnitude of a Complex Number zxiy zsquare root of xA2yquot2 Modulus Trigonometry zsquare root of xA2yquot2r xrcos theta yrsin theta zrcos theta isin thetaPolar Form of a Complex Number Product Rule for Complex Numbers z 1 gt 22r1r2 cos thetaltheta2 isin thetaltheta2 De Moivre s Theorem gt If zr cos theta isin theta then for any integer n zquotnrquotncos ntheta rsin ntheta

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