Content Skills Assessments Lessons. Identify, classify, and apply properties of negative and positive angles.
|
|
- Conrad Cain
- 5 years ago
- Views:
Transcription
1 Tachr: CORE TRIGONOMETRY Yar: Cours: TRIGONOMETRY Month: All Months S p t m b r Angls Essntial Qustions Can I idntify draw ngativ positiv angls in stard position? Do I hav a working knowldg of Basic Trigonomtry vocabulary? Can I dscrib th rlationship btwn angl masurs in dgrs radians? Contnt Skills Assssmnts Lssons Trms - initial sid, trminal sid, positiv/ngativ, stard position Angl Masurmnt in Dgrs Quadrantal Angls Cotrminal Angls Trigonomtric Functions Idntify, classify, apply proprtis of ngativ positiv angls. Convrt angl masurs from dgrs to radians. Angl Writ Masurmnt in angl Radians: masurs dfining, in dgrs, convrting to minuts, from, arc lngth sconds. Quizzs 9/1/2012 Homwork 9/1/2012 Tachr Obsrvation Qustioning 9/1/2012 Larning Bnchmarks Stards Studnts will undrst b abl to us trig vocabulary. 12.M.01- Masurmnt ~ Dscrib th rlationship btwn dgr radian masurs, us radian masur in th solution of problms, in particular, problms involving angular vlocity acclration. 12.M.02- Masurmnt ~ Us dimnsional analysis for unit convrsion to confirm that xprssions quations mak sns.
2 Essntial Qustions Can I dfin th 6 functions in trms of x, y, r? Can I idntify us rfrnc angls? Can I apply th corrct sign valu for ach trig function in ach Quadrant? Right Triangls Contnt Skills Assssmnts Lssons Sign valu for ach trig functions in ach quadrant. Scant, Coscant, Cotangnt Dfin apply th rciprocal functions, sc, csc, cot. Dfin th 6 trig functions in trms of x, y, r. Dfin us rfrnc triangls to crat a rfrnc triangls. Apply th appropriat sign valu for ach trig function in ach quadrant. Quizzs Homwork Tachr Obsrvation Qustioning Tsts Larning Bnchmarks Stards Studnt will undrst hav a working knowldg of basic trig functions. 12.G.01- Gomtry ~ Dfin th sin, cosin, tangnt of an acut angl. Apply to th solution of problms. 12.G.03- Gomtry ~ Us th notion of vctors to solv problms. Dscrib addition of vctors multiplication of a vctor by a scalar, both symbolically gomtrically. Us vctor mthods to obtain gomtric rsults. Essntial Qustions Can I us a varity of tchniqus to solv for triangls? Contnt Skills Assssmnts Lssons Pythagoran Thorm Spcial Right Triangls Right Apply th Pythagoran Thorm to solv for th lngths of a sid of a Quizzs 10/4/2012 Homwork 10/4/2012 Tachr obsrvation Larning Bnchmarks Stards Studnts will b abl to us trig to solv right triangls. 12.G.01- Gomtry ~ Dfin th sin, cosin, tangnt
3 Am I abl to apply th basic functions? Triangl Trigonomtry: Sin, Cos,Tan right triangl. Apply proprtis of spcial right triangls to Application of Right Can I dscrib Triangl solv convy an Trigonomtry; triangls. undrsting angls of of th Basic lvation Trigonomtric dprssion Functions? Find valus of functions using a calculator. qustioning. 10/4/2012 Studnts of an acut will b abl angl. to apply trig Apply to to solv th solution ral-world of problms. problms. Us trig functions solv for angls sid lngths of right triangls. Us trig functions to solv ral world application problms. O c t o b r Non-Right Triangls Essntial Qustions Can I us a varity of tchniqus to solv for triangls? Can I apply th functions? Contnt Skills Assssmnts Lssons Law of Sins Cosins Ara of Triangls Hron's Formula Idntify apply th Law of Sins Cosins to solv problms. Find th ara of a triangl Quizzs Homwork Tachr Obsrvation Qustioning Larning Bnchmarks Stards Studnts will b abl to us a varity of tchniqus to solv, to find th ara of, triangls. 12.G.01- Gomtry ~ Dfin th sin, cosin, tangnt of an acut angl. Apply to th solution of
4 N o v m b r Graphing Essntial Qustions Can I analyz th graphs of functions? Vctors using k=1/2absinc. Us apply Hron's formula. Contnt Skills Assssmnts Lssons Graphs of Sin Cosin Trms; Amplitud, Vrtical Shift, Priod, Phas Shift Introduc tangnt graphs. Idntify classify graphs of sin cosin. Crat graphs of sin cosin givn th quation or othr ssntial information. Idntify th amplitud, Priod, Shifts of a graph. Quizzs 12/31/2012 Homwork 12/31/2012 Tachr obsrvation qustioning 12/31/2012 problms. 12.G.02- Gomtry ~ Driv apply basic idntitis (.g., sin2q + cos2q = 1, tan2q + 1 = sc2q) th laws of sins cosins. Larning Bnchmarks Stards Studnts will b abl to analyz graph trig functions. 12.G.04- Gomtry ~ Rlat gomtric algbraic rprsntations of lins, simpl curvs, conic sctions. 12.P.13- Rlations Algbra ~ Dscrib th translations scal changs of a givn function Æ (x) rsulting from substitutions for th various paramtrs a, b, c, d in y = aæ (b(x +
5 D c m b r Idntitis Essntial Qustions Can I idntify Trigonomtric, Rciprocal, Pythagoran Idntitis? Can I apply th proprtis of Idntitis to solv problms? Can I prov Basic Idntitis c/b)) + d. In particular, dscrib th ffct of such changs on polynomial, rational, xponntial, logarithmic, functions. Contnt Skills Assssmnts Lssons Larning Bnchmarks Stards Trigonomtric, Dfin Rciprocal, Idntify th Pythagoran Idntitis. Proofs of Basic Idntitis. Trigonomtric, Rciprocal, Pythagoran Idntitis. Manipulat idntitis to solv problms. Prov Basic Idntitis. Quizzs Unit Tst Homwork Studnts will b abl 12.G.02- to prov Gomtry ~ basic trig Driv idntitis apply basic will us idntitis to idntitis solv trig (.g., sin2q + quations. cos2q = 1, tan2q + 1 = sc2q) th laws of sins cosins. 12.P.04- Rlations Algbra ~ Dmonstrat an undrsting of th, xponntial, logarithmic functions.
6 12.P.05- Rlations Algbra ~ Prform oprations on functions, including composition. Find invrss of functions. 12.P.08- Rlations Algbra ~ Solv a varity of quations inqualitis using algbraic, graphical, numrical mthods, including th quadratic formula; us tchnology whr appropriat. Includ polynomial, xponntial, logarithmic, functions; xprssions involving absolut valus; rlations; simpl rational
7 Trigonomtric Equations Essntial Qustions Can I apply Basic Trig Idntitis to solv quations? Am I abl to dmonstrat a varity of mthods usd to solv trig quations? Contnt Skills Assssmnts Lssons Trig Equations with Basic Idntitis Solving Trig Equations using Algbra Graphing Quizzs Homwork Final Exam xprssions. Larning Bnchmarks Stards Studnts will b abl to solv trig quations. 12.P.04- Rlations Algbra ~ Dmonstrat an undrsting of th, xponntial, logarithmic functions. 12.P.05- Rlations Algbra ~ Prform oprations on functions, including composition. Find invrss of functions. 12.P.06- Rlations Algbra ~ Givn algbraic, numric /or graphical rprsntations, rcogniz functions as polynomial, rational, logarithmic, xponntial, or. 12.P.08-
8 Rlations Algbra ~ Solv a varity of quations inqualitis using algbraic, graphical, numrical mthods, including th quadratic formula; us tchnology whr appropriat. Includ polynomial, xponntial, logarithmic, functions; xprssions involving absolut valus; rlations; simpl rational xprssions. 12.P.11- Rlations Algbra ~ Solv vryday problms that can b modld using polynomial, rational, xponntial, logarithmic,, stp functions,
9 J a n u a r y Rviw Essntial Qustions Can I solv both right nonright triangls? Do I undrst th bhavior of th trig functions? Am I abl to apply trig idntitis to simplify xprssions to solv quations? Contnt Skills Assssmnts Lssons absolut valus, squar roots. Apply appropriat graphical, tabular, or symbolic mthods to th solution. Includ growth dcay; joint (.g., I = Prt, y = k(w1 + w2)) combind (F = G(m1m2)/d2) variation, priodic procsss. Larning Bnchmarks Stards Can th studnt solv both right nonright triangls? Can th studnt apply trig idntitis to simplify xprssions solv quations? Can th studnt solv ral-world applications, scinc in particular?
10 Am I abl to tak a problm rcogniz whn which mthods of trig ar ncssary? Can th studnt solv ral-world applications, scinc in particular? Can I analyz intrprt graphs?
5. B To determine all the holes and asymptotes of the equation: y = bdc dced f gbd
1. First you chck th domain of g x. For this function, x cannot qual zro. Thn w find th D domain of f g x D 3; D 3 0; x Q x x 1 3, x 0 2. Any cosin graph is going to b symmtric with th y-axis as long as
More informationJOHNSON COUNTY COMMUNITY COLLEGE Calculus I (MATH 241) Final Review Fall 2016
JOHNSON COUNTY COMMUNITY COLLEGE Calculus I (MATH ) Final Rviw Fall 06 Th Final Rviw is a starting point as you study for th final am. You should also study your ams and homwork. All topics listd in th
More informationDSP-First, 2/e. LECTURE # CH2-3 Complex Exponentials & Complex Numbers TLH MODIFIED. Aug , JH McClellan & RW Schafer
DSP-First, / TLH MODIFIED LECTURE # CH-3 Complx Exponntials & Complx Numbrs Aug 016 1 READING ASSIGNMENTS This Lctur: Chaptr, Scts. -3 to -5 Appndix A: Complx Numbrs Complx Exponntials Aug 016 LECTURE
More informationThe graph of y = x (or y = ) consists of two branches, As x 0, y + ; as x 0, y +. x = 0 is the
Copyright itutcom 005 Fr download & print from wwwitutcom Do not rproduc by othr mans Functions and graphs Powr functions Th graph of n y, for n Q (st of rational numbrs) y is a straight lin through th
More informationSan José State University Aerospace Engineering AE 138 Vector-Based Dynamics for Aerospace Applications, Fall 2016
San José Stat Univrsity Arospac Enginring AE 138 Vctor-Basd Dynamics for Arospac Applications, Fall 2016 Instructor: Offic Location: Email: Offic Hours: Class Days/Tim: Classroom: Prof. J.M. Huntr E272F
More informationThings I Should Know Before I Get to Calculus Class
Things I Should Know Bfor I Gt to Calculus Class Quadratic Formula = b± b 4ac a sin + cos = + tan = sc + cot = csc sin( ± y ) = sin cos y ± cos sin y cos( + y ) = cos cos y sin sin y cos( y ) = cos cos
More informationSundials and Linear Algebra
Sundials and Linar Algbra M. Scot Swan July 2, 25 Most txts on crating sundials ar dirctd towards thos who ar solly intrstd in making and using sundials and usually assums minimal mathmatical background.
More informationFirst derivative analysis
Robrto s Nots on Dirntial Calculus Chaptr 8: Graphical analysis Sction First drivativ analysis What you nd to know alrady: How to us drivativs to idntiy th critical valus o a unction and its trm points
More informationMathematics. Complex Number rectangular form. Quadratic equation. Quadratic equation. Complex number Functions: sinusoids. Differentiation Integration
Mathmatics Compl numbr Functions: sinusoids Sin function, cosin function Diffrntiation Intgration Quadratic quation Quadratic quations: a b c 0 Solution: b b 4ac a Eampl: 1 0 a= b=- c=1 4 1 1or 1 1 Quadratic
More information2008 AP Calculus BC Multiple Choice Exam
008 AP Multipl Choic Eam Nam 008 AP Calculus BC Multipl Choic Eam Sction No Calculator Activ AP Calculus 008 BC Multipl Choic. At tim t 0, a particl moving in th -plan is th acclration vctor of th particl
More informationSolution: APPM 1360 Final (150 pts) Spring (60 pts total) The following parts are not related, justify your answers:
APPM 6 Final 5 pts) Spring 4. 6 pts total) Th following parts ar not rlatd, justify your answrs: a) Considr th curv rprsntd by th paramtric quations, t and y t + for t. i) 6 pts) Writ down th corrsponding
More informationPROOF OF FIRST STANDARD FORM OF NONELEMENTARY FUNCTIONS
Intrnational Journal Of Advanc Rsarch In Scinc And Enginring http://www.ijars.com IJARSE, Vol. No., Issu No., Fbruary, 013 ISSN-319-8354(E) PROOF OF FIRST STANDARD FORM OF NONELEMENTARY FUNCTIONS 1 Dharmndra
More informationThomas Whitham Sixth Form
Thomas Whitham Sith Form Pur Mathmatics Unit C Algbra Trigonomtr Gomtr Calculus Vctor gomtr Pag Algbra Molus functions graphs, quations an inqualitis Graph of f () Draw f () an rflct an part of th curv
More informationMSLC Math 151 WI09 Exam 2 Review Solutions
Eam Rviw Solutions. Comput th following rivativs using th iffrntiation ruls: a.) cot cot cot csc cot cos 5 cos 5 cos 5 cos 5 sin 5 5 b.) c.) sin( ) sin( ) y sin( ) ln( y) ln( ) ln( y) sin( ) ln( ) y y
More informationA. Limits and Horizontal Asymptotes ( ) f x f x. f x. x "±# ( ).
A. Limits and Horizontal Asymptots What you ar finding: You can b askd to find lim x "a H.A.) problm is asking you find lim x "# and lim x "$#. or lim x "±#. Typically, a horizontal asymptot algbraically,
More informationDifferentiation of Exponential Functions
Calculus Modul C Diffrntiation of Eponntial Functions Copyright This publication Th Northrn Albrta Institut of Tchnology 007. All Rights Rsrvd. LAST REVISED March, 009 Introduction to Diffrntiation of
More informationReview of Exponentials and Logarithms - Classwork
Rviw of Eponntials and Logarithms - Classwork In our stud of calculus, w hav amind drivativs and intgrals of polnomial prssions, rational prssions, and trignomtric prssions. What w hav not amind ar ponntial
More informationMath 34A. Final Review
Math A Final Rviw 1) Us th graph of y10 to find approimat valus: a) 50 0. b) y (0.65) solution for part a) first writ an quation: 50 0. now tak th logarithm of both sids: log() log(50 0. ) pand th right
More informationCalculus concepts derivatives
All rasonabl fforts hav bn mad to mak sur th nots ar accurat. Th author cannot b hld rsponsibl for any damags arising from th us of ths nots in any fashion. Calculus concpts drivativs Concpts involving
More informationSECTION where P (cos θ, sin θ) and Q(cos θ, sin θ) are polynomials in cos θ and sin θ, provided Q is never equal to zero.
SETION 6. 57 6. Evaluation of Dfinit Intgrals Exampl 6.6 W hav usd dfinit intgrals to valuat contour intgrals. It may com as a surpris to larn that contour intgrals and rsidus can b usd to valuat crtain
More information4. (5a + b) 7 & x 1 = (3x 1)log 10 4 = log (M1) [4] d = 3 [4] T 2 = 5 + = 16 or or 16.
. 7 7 7... 7 7 (n )0 7 (M) 0(n ) 00 n (A) S ((7) 0(0)) (M) (7 00) 8897 (A). (5a b) 7 7... (5a)... (M) 7 5 5 (a b ) 5 5 a b (M)(A) So th cofficint is 75 (A) (C) [] S (7 7) (M) () 8897 (A) (C) [] 5. x.55
More informationMor Tutorial at www.dumblittldoctor.com Work th problms without a calculator, but us a calculator to chck rsults. And try diffrntiating your answrs in part III as a usful chck. I. Applications of Intgration
More informationA Propagating Wave Packet Group Velocity Dispersion
Lctur 8 Phys 375 A Propagating Wav Packt Group Vlocity Disprsion Ovrviw and Motivation: In th last lctur w lookd at a localizd solution t) to th 1D fr-particl Schrödingr quation (SE) that corrsponds to
More information1997 AP Calculus AB: Section I, Part A
997 AP Calculus AB: Sction I, Part A 50 Minuts No Calculator Not: Unlss othrwis spcifid, th domain of a function f is assumd to b th st of all ral numbrs for which f () is a ral numbr.. (4 6 ) d= 4 6 6
More informationGrade 12 (MCV4UE) AP Calculus Page 1 of 5 Derivative of a Function & Differentiability
Gra (MCV4UE) AP Calculus Pag of 5 Drivativ of a Function & Diffrntiabilit Th Drivativ at a Point f ( a h) f ( a) Rcall, lim provis th slop of h0 h th tangnt to th graph f ( at th point a, f ( a), an th
More information1973 AP Calculus AB: Section I
97 AP Calculus AB: Sction I 9 Minuts No Calculator Not: In this amination, ln dnots th natural logarithm of (that is, logarithm to th bas ).. ( ) d= + C 6 + C + C + C + C. If f ( ) = + + + and ( ), g=
More informationEXST Regression Techniques Page 1
EXST704 - Rgrssion Tchniqus Pag 1 Masurmnt rrors in X W hav assumd that all variation is in Y. Masurmnt rror in this variabl will not ffct th rsults, as long as thy ar uncorrlatd and unbiasd, sinc thy
More informationObjective Mathematics
x. Lt 'P' b a point on th curv y and tangnt x drawn at P to th curv has gratst slop in magnitud, thn point 'P' is,, (0, 0),. Th quation of common tangnt to th curvs y = 6 x x and xy = x + is : x y = 8
More informationChapter two Functions
Chaptr two Functions -- Eponntial Logarithm functions Eponntial functions If a is a positiv numbr is an numbr, w dfin th ponntial function as = a with domain - < < ang > Th proprtis of th ponntial functions
More informationThomas Whitham Sixth Form
Thomas Whitham Sith Form Pur Mathmatics Cor rvision gui Pag Algbra Moulus functions graphs, quations an inqualitis Graph of f () Draw f () an rflct an part of th curv blow th ais in th ais. f () f () f
More informationSection 11.6: Directional Derivatives and the Gradient Vector
Sction.6: Dirctional Drivativs and th Gradint Vctor Practic HW rom Stwart Ttbook not to hand in p. 778 # -4 p. 799 # 4-5 7 9 9 35 37 odd Th Dirctional Drivativ Rcall that a b Slop o th tangnt lin to th
More informationQuasi-Classical States of the Simple Harmonic Oscillator
Quasi-Classical Stats of th Simpl Harmonic Oscillator (Draft Vrsion) Introduction: Why Look for Eignstats of th Annihilation Oprator? Excpt for th ground stat, th corrspondnc btwn th quantum nrgy ignstats
More informationMATH 319, WEEK 15: The Fundamental Matrix, Non-Homogeneous Systems of Differential Equations
MATH 39, WEEK 5: Th Fundamntal Matrix, Non-Homognous Systms of Diffrntial Equations Fundamntal Matrics Considr th problm of dtrmining th particular solution for an nsmbl of initial conditions For instanc,
More informationare given in the table below. t (hours)
CALCULUS WORKSHEET ON INTEGRATION WITH DATA Work th following on notbook papr. Giv dcimal answrs corrct to thr dcimal placs.. A tank contains gallons of oil at tim t = hours. Oil is bing pumpd into th
More informationSlide 1. Slide 2. Slide 3 DIGITAL SIGNAL PROCESSING CLASSIFICATION OF SIGNALS
Slid DIGITAL SIGAL PROCESSIG UIT I DISCRETE TIME SIGALS AD SYSTEM Slid Rviw of discrt-tim signals & systms Signal:- A signal is dfind as any physical quantity that varis with tim, spac or any othr indpndnt
More informationExercise 1. Sketch the graph of the following function. (x 2
Writtn tst: Fbruary 9th, 06 Exrcis. Sktch th graph of th following function fx = x + x, spcifying: domain, possibl asymptots, monotonicity, continuity, local and global maxima or minima, and non-drivability
More informationA=P=E M-A=N Alpha particle Beta Particle. Periodic table
Nam Pr. Atomic Structur/Nuclar Chmistry (Ch. 3 & 21) OTHS Acadmic Chmistry Objctivs: Undrstand th xprimntal dsign and conclusions usd in th dvlopmnt of modrn atomic thory, including Dalton's Postulats,
More information7.4 Potential Difference and Electric Potential
7.4 Potntial Diffrnc and Elctric Potntial In th prvious sction, you larnd how two paralll chargd surfacs produc a uniform lctric fild. From th dfinition of an lctric fild as a forc acting on a charg, it
More information4 x 4, and. where x is Town Square
Accumulation and Population Dnsity E. A city locatd along a straight highway has a population whos dnsity can b approimatd by th function p 5 4 th distanc from th town squar, masurd in mils, whr 4 4, and
More information1997 AP Calculus AB: Section I, Part A
997 AP Calculus AB: Sction I, Part A 50 Minuts No Calculator Not: Unlss othrwis spcifid, th domain of a function f is assumd to b th st of all ral numbrs x for which f (x) is a ral numbr.. (4x 6 x) dx=
More informationAnnounce. ECE 2026 Summer LECTURE OBJECTIVES READING. LECTURE #3 Complex View of Sinusoids May 21, Complex Number Review
ECE 06 Summr 018 Announc HW1 du at bginning of your rcitation tomorrow Look at HW bfor rcitation Lab 1 is Thursday: Com prpard! Offic hours hav bn postd: LECTURE #3 Complx Viw of Sinusoids May 1, 018 READIG
More informationLinear-Phase FIR Transfer Functions. Functions. Functions. Functions. Functions. Functions. Let
It is impossibl to dsign an IIR transfr function with an xact linar-phas It is always possibl to dsign an FIR transfr function with an xact linar-phas rspons W now dvlop th forms of th linarphas FIR transfr
More informationDIFFERENTIAL EQUATION
MD DIFFERENTIAL EQUATION Sllabus : Ordinar diffrntial quations, thir ordr and dgr. Formation of diffrntial quations. Solution of diffrntial quations b th mthod of sparation of variabls, solution of homognous
More informationTrigonometric functions
Robrto s Nots on Diffrntial Calculus Captr 5: Drivativs of transcndntal functions Sction 5 Drivativs of Trigonomtric functions Wat you nd to know alrady: Basic trigonomtric limits, t dfinition of drivativ,
More informationMassachusetts Institute of Technology Department of Mechanical Engineering
Massachustts Institut of Tchnolog Dpartmnt of Mchanical Enginring. Introduction to Robotics Mid-Trm Eamination Novmbr, 005 :0 pm 4:0 pm Clos-Book. Two shts of nots ar allowd. Show how ou arrivd at our
More informationThe Matrix Exponential
Th Matrix Exponntial (with xrciss) by D. Klain Vrsion 207.0.05 Corrctions and commnts ar wlcom. Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial of A to b th matrix A A k I + A + k!
More informationHigher order derivatives
Robrto s Nots on Diffrntial Calculus Chaptr 4: Basic diffrntiation ruls Sction 7 Highr ordr drivativs What you nd to know alrady: Basic diffrntiation ruls. What you can larn hr: How to rpat th procss of
More informationAP Calculus BC AP Exam Problems Chapters 1 3
AP Eam Problms Captrs Prcalculus Rviw. If f is a continuous function dfind for all ral numbrs and if t maimum valu of f() is 5 and t minimum valu of f() is 7, tn wic of t following must b tru? I. T maimum
More informationData Assimilation 1. Alan O Neill National Centre for Earth Observation UK
Data Assimilation 1 Alan O Nill National Cntr for Earth Obsrvation UK Plan Motivation & basic idas Univariat (scalar) data assimilation Multivariat (vctor) data assimilation 3d-Variational Mthod (& optimal
More informationThe Matrix Exponential
Th Matrix Exponntial (with xrciss) by Dan Klain Vrsion 28928 Corrctions and commnts ar wlcom Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial of A to b th matrix () A A k I + A + k!
More informationν a (p e ) p e fpt(a) = lim
THE F -PURE THRESHOLD OF AN ELLIPTIC CURVE BHARGAV BHATT ABSTRACT. W calculat th F -pur thrshold of th affin con on an lliptic curv in a fixd positiv charactristic p. Th mthod mployd is dformation-thortic,
More informationGeneral Notes About 2007 AP Physics Scoring Guidelines
AP PHYSICS C: ELECTRICITY AND MAGNETISM 2007 SCORING GUIDELINES Gnral Nots About 2007 AP Physics Scoring Guidlins 1. Th solutions contain th most common mthod of solving th fr-rspons qustions and th allocation
More informationas a derivative. 7. [3.3] On Earth, you can easily shoot a paper clip straight up into the air with a rubber band. In t sec
MATH6 Fall 8 MIDTERM II PRACTICE QUESTIONS PART I. + if
More informationCPSC 665 : An Algorithmist s Toolkit Lecture 4 : 21 Jan Linear Programming
CPSC 665 : An Algorithmist s Toolkit Lctur 4 : 21 Jan 2015 Lcturr: Sushant Sachdva Linar Programming Scrib: Rasmus Kyng 1. Introduction An optimization problm rquirs us to find th minimum or maximum) of
More informationMATH 1080 Test 2-SOLUTIONS Spring
MATH Tst -SOLUTIONS Spring 5. Considr th curv dfind by x = ln( 3y + 7) on th intrval y. a. (5 points) St up but do not simplify or valuat an intgral rprsnting th lngth of th curv on th givn intrval. =
More informationNote If the candidate believes that e x = 0 solves to x = 0 or gives an extra solution of x = 0, then withhold the final accuracy mark.
. (a) Eithr y = or ( 0, ) (b) Whn =, y = ( 0 + ) = 0 = 0 ( + ) = 0 ( )( ) = 0 Eithr = (for possibly abov) or = A 3. Not If th candidat blivs that = 0 solvs to = 0 or givs an tra solution of = 0, thn withhold
More informationx = (c) = -----
R ainbows hav bn a sourc of aw and inspiration throughout history. Many ancint popls saw thm as bridgs to th gods. ncint Pruvians hld thm in such wondr that thy rmaind silnt whil rainbows wr in th sky.
More informationCOHORT MBA. Exponential function. MATH review (part2) by Lucian Mitroiu. The LOG and EXP functions. Properties: e e. lim.
MTH rviw part b Lucian Mitroiu Th LOG and EXP functions Th ponntial function p : R, dfind as Proprtis: lim > lim p Eponntial function Y 8 6 - -8-6 - - X Th natural logarithm function ln in US- log: function
More informationDeift/Zhou Steepest descent, Part I
Lctur 9 Dift/Zhou Stpst dscnt, Part I W now focus on th cas of orthogonal polynomials for th wight w(x) = NV (x), V (x) = t x2 2 + x4 4. Sinc th wight dpnds on th paramtr N N w will writ π n,n, a n,n,
More informationMath-3. Lesson 5-6 Euler s Number e Logarithmic and Exponential Modeling (Newton s Law of Cooling)
Math-3 Lsson 5-6 Eulr s Numbr Logarithmic and Eponntial Modling (Nwton s Law of Cooling) f ( ) What is th numbr? is th horizontal asymptot of th function: 1 1 ~ 2.718... On my 3rd submarin (USS Springfild,
More information10. The Discrete-Time Fourier Transform (DTFT)
Th Discrt-Tim Fourir Transform (DTFT Dfinition of th discrt-tim Fourir transform Th Fourir rprsntation of signals plays an important rol in both continuous and discrt signal procssing In this sction w
More informationIntroduction to the Fourier transform. Computer Vision & Digital Image Processing. The Fourier transform (continued) The Fourier transform (continued)
Introduction to th Fourir transform Computr Vision & Digital Imag Procssing Fourir Transform Lt f(x) b a continuous function of a ral variabl x Th Fourir transform of f(x), dnotd by I {f(x)} is givn by:
More informationThere is an arbitrary overall complex phase that could be added to A, but since this makes no difference we set it to zero and choose A real.
Midtrm #, Physics 37A, Spring 07. Writ your rsponss blow or on xtra pags. Show your work, and tak car to xplain what you ar doing; partial crdit will b givn for incomplt answrs that dmonstrat som concptual
More information2/12/2013. Overview. 12-Power Transmission Text: Conservation of Complex Power. Introduction. Power Transmission-Short Line
//03 Ovrviw -owr Transmission Txt: 4.6-4.0 ECEGR 45 owr ystms Consrvation of Complx owr hort in owr Transmission owr Transmission isualization Radial in Mdium and ong in owr Transmission oltag Collaps
More informationEE140 Introduction to Communication Systems Lecture 2
EE40 Introduction to Communication Systms Lctur 2 Instructor: Prof. Xiliang Luo ShanghaiTch Univrsity, Spring 208 Architctur of a Digital Communication Systm Transmittr Sourc A/D convrtr Sourc ncodr Channl
More informationLaboratory work # 8 (14) EXPERIMENTAL ESTIMATION OF CRITICAL STRESSES IN STRINGER UNDER COMPRESSION
Laboratory wor # 8 (14) XPRIMNTAL STIMATION OF CRITICAL STRSSS IN STRINGR UNDR COMPRSSION At action of comprssing ffort on a bar (column, rod, and stringr) two inds of loss of stability ar possibl: 1)
More informationY 0. Standing Wave Interference between the incident & reflected waves Standing wave. A string with one end fixed on a wall
Staning Wav Intrfrnc btwn th incint & rflct wavs Staning wav A string with on n fix on a wall Incint: y, t) Y cos( t ) 1( Y 1 ( ) Y (St th incint wav s phas to b, i.., Y + ral & positiv.) Rflct: y, t)
More information6 th Grade Math. Course Description
Course Description The sixth grade general mathematics course continues the development of the skills and concepts taught at the elementary level. Applications, problem solving, and critical thinking are
More informationIndeterminate Forms and L Hôpital s Rule. Indeterminate Forms
SECTION 87 Intrminat Forms an L Hôpital s Rul 567 Sction 87 Intrminat Forms an L Hôpital s Rul Rcogniz its that prouc intrminat forms Apply L Hôpital s Rul to valuat a it Intrminat Forms Rcall from Chaptrs
More informationPrelim Examination 2011 / 2012 (Assessing Units 1 & 2) MATHEMATICS. Advanced Higher Grade. Time allowed - 2 hours
Prlim Eamination / (Assssing Units & ) MATHEMATICS Advancd Highr Grad Tim allowd - hours Rad Carfull. Calculators ma b usd in this papr.. Candidats should answr all qustions. Full crdit will onl b givn
More information(Upside-Down o Direct Rotation) β - Numbers
Amrican Journal of Mathmatics and Statistics 014, 4(): 58-64 DOI: 10593/jajms0140400 (Upsid-Down o Dirct Rotation) β - Numbrs Ammar Sddiq Mahmood 1, Shukriyah Sabir Ali,* 1 Dpartmnt of Mathmatics, Collg
More informationComplex representation of continuous-time periodic signals
. Complx rprsntation of continuous-tim priodic signals Eulr s quation jwt cost jsint his is th famous Eulr s quation. Brtrand Russll and Richard Fynman both gav this quation plntiful prais with words such
More informationFunction Spaces. a x 3. (Letting x = 1 =)) a(0) + b + c (1) = 0. Row reducing the matrix. b 1. e 4 3. e 9. >: (x = 1 =)) a(0) + b + c (1) = 0
unction Spacs Prrquisit: Sction 4.7, Coordinatization n this sction, w apply th tchniqus of Chaptr 4 to vctor spacs whos lmnts ar functions. Th vctor spacs P n and P ar familiar xampls of such spacs. Othr
More informationSupplementary Materials
6 Supplmntary Matrials APPENDIX A PHYSICAL INTERPRETATION OF FUEL-RATE-SPEED FUNCTION A truck running on a road with grad/slop θ positiv if moving up and ngativ if moving down facs thr rsistancs: arodynamic
More information1 Isoparametric Concept
UNIVERSITY OF CALIFORNIA BERKELEY Dpartmnt of Civil Enginring Spring 06 Structural Enginring, Mchanics and Matrials Profssor: S. Govindj Nots on D isoparamtric lmnts Isoparamtric Concpt Th isoparamtric
More information1 1 1 p q p q. 2ln x x. in simplest form. in simplest form in terms of x and h.
NAME SUMMER ASSIGNMENT DUE SEPTEMBER 5 (FIRST DAY OF SCHOOL) AP CALC AB Dirctions: Answr all of th following qustions on a sparat sht of papr. All work must b shown. You will b tstd on this matrial somtim
More informationCENTRAL TEXAS COLLEGE SYLLABUS FOR MATH 2414 CALCULUS II. Semester Hours Credit: 4
CENTRAL TEXAS COLLEGE SYLLABUS FOR MATH 2414 CALCULUS II Smstr Hours Crdit: 4 I. INTRODUCTION A. Calculus II is a continuation of Calculus I. This cours mphasizs diffrntial quations; applications of intgration;
More information3 Finite Element Parametric Geometry
3 Finit Elmnt Paramtric Gomtry 3. Introduction Th intgral of a matrix is th matrix containing th intgral of ach and vry on of its original componnts. Practical finit lmnt analysis rquirs intgrating matrics,
More information2013 Specialist Mathematics GA 3: Written examination 2
0 0 Spcialist Mathmatics GA : Writtn xamination GENERAL COMMENTS Th 0 Spcialist Mathmatics xamination comprisd multipl-choic qustions (worth marks) and fiv xtndd qustions (worth 8 marks). Th papr smd accssibl
More information3 2x. 3x 2. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
Math B Intgration Rviw (Solutions) Do ths intgrals. Solutions ar postd at th wbsit blow. If you hav troubl with thm, sk hlp immdiatly! () 8 d () 5 d () d () sin d (5) d (6) cos d (7) d www.clas.ucsb.du/staff/vinc
More informationON THE DISTRIBUTION OF THE ELLIPTIC SUBSET SUM GENERATOR OF PSEUDORANDOM NUMBERS
INTEGERS: ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 8 2008, #A3 ON THE DISTRIBUTION OF THE ELLIPTIC SUBSET SUM GENERATOR OF PSEUDORANDOM NUMBERS Edwin D. El-Mahassni Dpartmnt of Computing, Macquari
More informationFourier Transforms and the Wave Equation. Key Mathematics: More Fourier transform theory, especially as applied to solving the wave equation.
Lur 7 Fourir Transforms and th Wav Euation Ovrviw and Motivation: W first discuss a fw faturs of th Fourir transform (FT), and thn w solv th initial-valu problm for th wav uation using th Fourir transform
More informationAddition of angular momentum
Addition of angular momntum April, 0 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat th
More informationWhat is the product of an integer multiplied by zero? and divided by zero?
IMP007 Introductory Math Cours 3. ARITHMETICS AND FUNCTIONS 3.. BASIC ARITHMETICS REVIEW (from GRE) Which numbrs form th st of th Intgrs? What is th product of an intgr multiplid by zro? and dividd by
More informationSTABILITY ANALYSIS OF FUZZY CONTROLLERS USING THE MODIFIED POPOV CRITERION
SABILIY ANALYSIS OF FUZZY CONROLLERS USING HE MODIFIED POPOV CRIERION Mauricio Gonçalvs Santana Junior Instituto cnológico d Aronáutica Pça Mal Eduardo Goms, 50 Vila das Acácias - CEP 2228-900 São José
More information2.3 Matrix Formulation
23 Matrix Formulation 43 A mor complicatd xampl ariss for a nonlinar systm of diffrntial quations Considr th following xampl Exampl 23 x y + x( x 2 y 2 y x + y( x 2 y 2 (233 Transforming to polar coordinats,
More information4037 ADDITIONAL MATHEMATICS
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Lvl MARK SCHEME for th Octobr/Novmbr 0 sris 40 ADDITIONAL MATHEMATICS 40/ Papr, maimum raw mark 80 This mark schm is publishd as an aid to tachrs and candidats,
More informationCHAPTER 1. Introductory Concepts Elements of Vector Analysis Newton s Laws Units The basis of Newtonian Mechanics D Alembert s Principle
CHPTER 1 Introductory Concpts Elmnts of Vctor nalysis Nwton s Laws Units Th basis of Nwtonian Mchanics D lmbrt s Principl 1 Scinc of Mchanics: It is concrnd with th motion of matrial bodis. odis hav diffrnt
More informationCOMPUTER GENERATED HOLOGRAMS Optical Sciences 627 W.J. Dallas (Monday, April 04, 2005, 8:35 AM) PART I: CHAPTER TWO COMB MATH.
C:\Dallas\0_Courss\03A_OpSci_67\0 Cgh_Book\0_athmaticalPrliminaris\0_0 Combath.doc of 8 COPUTER GENERATED HOLOGRAS Optical Scincs 67 W.J. Dallas (onday, April 04, 005, 8:35 A) PART I: CHAPTER TWO COB ATH
More informationu 3 = u 3 (x 1, x 2, x 3 )
Lctur 23: Curvilinar Coordinats (RHB 8.0 It is oftn convnint to work with variabls othr than th Cartsian coordinats x i ( = x, y, z. For xampl in Lctur 5 w mt sphrical polar and cylindrical polar coordinats.
More informationSelf-Adjointness and Its Relationship to Quantum Mechanics. Ronald I. Frank 2016
Ronald I. Frank 06 Adjoint https://n.wikipdia.org/wiki/adjoint In gnral thr is an oprator and a procss that dfin its adjoint *. It is thn slf-adjoint if *. Innr product spac https://n.wikipdia.org/wiki/innr_product_spac
More informationME 321 Kinematics and Dynamics of Machines S. Lambert Winter 2002
3.4 Forc Analysis of Linkas An undrstandin of forc analysis of linkas is rquird to: Dtrmin th raction forcs on pins, tc. as a consqunc of a spcifid motion (don t undrstimat th sinificanc of dynamic or
More informationAddition of angular momentum
Addition of angular momntum April, 07 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat
More informationDealing with quantitative data and problem solving life is a story problem! Attacking Quantitative Problems
Daling with quantitati data and problm soling lif is a story problm! A larg portion of scinc inols quantitati data that has both alu and units. Units can sa your butt! Nd handl on mtric prfixs Dimnsional
More informationOutline. Thanks to Ian Blockland and Randy Sobie for these slides Lifetimes of Decaying Particles Scattering Cross Sections Fermi s Golden Rule
Outlin Thanks to Ian Blockland and andy obi for ths slids Liftims of Dcaying Particls cattring Cross ctions Frmi s Goldn ul Physics 424 Lctur 12 Pag 1 Obsrvabls want to rlat xprimntal masurmnts to thortical
More informationINTEGRATION BY PARTS
Mathmatics Rvision Guids Intgration by Parts Pag of 7 MK HOME TUITION Mathmatics Rvision Guids Lvl: AS / A Lvl AQA : C Edcl: C OCR: C OCR MEI: C INTEGRATION BY PARTS Vrsion : Dat: --5 Eampls - 6 ar copyrightd
More informationAn Extensive Study of Approximating the Periodic. Solutions of the Prey Predator System
pplid athmatical Scincs Vol. 00 no. 5 5 - n xtnsiv Study of pproximating th Priodic Solutions of th Pry Prdator Systm D. Vnu Gopala Rao * ailing addrss: Plot No.59 Sctor-.V.P.Colony Visahapatnam 50 07
More informationRandom Process Part 1
Random Procss Part A random procss t (, ζ is a signal or wavform in tim. t : tim ζ : outcom in th sampl spac Each tim w rapat th xprimnt, a nw wavform is gnratd. ( W will adopt t for short. Tim sampls
More informationCoupled Pendulums. Two normal modes.
Tim Dpndnt Two Stat Problm Coupld Pndulums Wak spring Two normal mods. No friction. No air rsistanc. Prfct Spring Start Swinging Som tim latr - swings with full amplitud. stationary M +n L M +m Elctron
More informationSec 2.3 Modeling with First Order Equations
Sc.3 Modling with First Ordr Equations Mathmatical modls charactriz physical systms, oftn using diffrntial quations. Modl Construction: Translating physical situation into mathmatical trms. Clarly stat
More information