# REVIEW, pages

Size: px
Start display at page:

Transcription

1 REVIEW, pges Point P(10, 4) is on the terminl rm of n ngle u in stndrd position. ) Determine the distnce of P from the origin. The distnce of P from the origin is r. r x 2 y 2 Substitute: x 10, y 4 r r 116, or 2 29 b) Write the primry trigonometric rtios of u. sin U y cos U x r r 2 5 4, or 10, or tn U y x 4, or c) Wht is the vlue of u to the nerest degree? tn U 0.4 U tn 1 (0.4) U U is pproximtely Angle u is in stndrd position with its terminl rm in Qudrnt 1 2 nd sin u = 3. ) Determine cos u nd tn u. r 2 x 2 y 2 Substitute: r 3, y x x 2 5 x 5 cos U x r 5 3 tn U y x 2 5 b) Determine the vlue of u to the nerest degree. sin U 2 3 P DO NOT COPY. U sin b U U is pproximtely 42. Chpter 6: Trigonometry Review Solutions 47

2 For ech ngle below: i) Sketch it in stndrd position. ii) Determine its reference ngle. ) 112 b) 286 i) Since the ngle is between i) Since the ngle is between 90 nd 180, the terminl 270 nd 360, the terminl rm is in Qudrnt 2. rm is in Qudrnt 4. y y O 112 x 286 O x ii) The ngle is in Qudrnt 2, ii) The ngle is in Qudrnt 4, so its reference ngle is: so its reference ngle is: To the nerest degree, which vlues of u stisfy the eqution 3 sin u =- 8 for 0 u 360? The reference ngle is: sin b sin U is negtive in Qudrnts 3 nd 4 so: U nd U In ABC, BC = 20 cm, AB = 25 cm, nd A = 45 Show tht is it possible to drw ABC, then determine if these mesurements illustrte n mbiguous cse. The rtio of the side opposite A to the side djcent to A is: BC 20, which is 0.8 AB 25 sin BC Since >sin 45, it is possible to drw tringle AB Since sin 45 <0.8<1, then this is n mbiguous cse 48 Chpter 6: Trigonometry Review Solutions DO NOT COPY. P

3 ) In ABC, AB = 18.7 cm, AC = 17.9 cm, nd B = 70 ; determine the mesure of BC to the nerest tenth of centimetre. Check for the mbiguous cse. The rtio of the side opposite B to the side djcent to B is: AC 17.9, which is AB 18.7 sin Since sin 70 < <1, then this is n mbiguous cse, nd 2 tringles cn be constructed: ABC 1 is cute; ABC 2 is obtuse. Sketch digrm. B A 18.7 cm 17.9 cm 70 C 2 C 1 This digrm is not drwn to scle. In ABC 1 In ABC 2 Determine C 1. C C 1 sin C 1 c sin B b Substitute: B 70, So, A 180 ( ) c 18.7, b sin C 1 sin sin 70 sin C C 1 sin sin 70 b 17.9 C So, A 180 ( ) sin A b sin B Substitute: A B 70, b sin sin sin sin sin A b sin B Substitute: A B 70, b sin sin sin sin So, BC 9.8 cm or 3.0 cm P DO NOT COPY. Chpter 6: Trigonometry Review Solutions 49

4 b) In PQR, QR = 20 cm, PQ = 17 cm, nd P = 50 ; determine the mesure of R to the nerest degree. Check for the mbiguous cse. The rtio of the side opposite P to the side djcent to P is: QR 20, which is greter thn 1, so only 1 tringle is possible PQ 17 Sketch digrm. Q sin R r sin P p Substitute: P 50, r 17, p cm 20 cm sin R sin sin 50 P sin R 20 Since R is cute: R sin 1 17 sin 50 b 20 R R 41 R 7. Two tow trucks, on stright rod, re pulling vehicle from field. The cble from one truck is let out 47 m nd it mkes n ngle of 60 with the rod. The cble from the other truck is let out 50 m. To the nerest metre, how fr prt re the trucks? Sketch digrm. T 60 S Check for the mbiguous cse. The rtio of the side opposite T to the side djcent to T is: 47 m 50 m SV 50, which is >1, so only 1 tringle TV 47 V is possible Determine S first. Then determine TS. sin S v sin V t s sin T t sin T Substitute: T 60, s 47, t 50 Substitute: V T 60, t 50 sin S sin sin 60 sin S 50 S sin 1 47 sin 60 b 50 v 50 sin sin sin v sin 60 v Since S is cute: The trucks re pproximtely S m prt. So, V 180 ( ) Chpter 6: Trigonometry Review Solutions DO NOT COPY. P

5 Determine ech indicted mesure to the nerest tenth of unit. ) 30.0 cm f 2 d 2 e 2 2de cos F E F 74 Substitute: d 30, e 21.3, F cm f (30)(21.3) cos 74 f D f (30)(21.3) cos 74 f f 31.6 cm b) G 18 cm 16 cm H J 15 cm j 2 g 2 h 2 2gh cos J Substitute: j 18, g 15, h (15)(16) cos J cos J (15)(16) J cos b 2(15)(16) J U In RST, R = 64, RS = 8.3 m, nd RT = 9.0 m Solve this tringle. Give the side lengths to the nerest tenth of metre nd the ngle mesures to the nerest degree. Since the given ngle is between the two given sides, only 1 tringle is possible. Sketch digrm. Determine ST first. 8.3 m r 2 s 2 t 2 2st cos R R S 64 Substitute: s 9, t 8.3, R 64 r (9)(8.3) cos m r (9)(8.3) cos 64 r Determine S. T sin S s sin R r Substitute: R 64, s 9, r sin S sin sin 64 sin S Since S is cute: S sin 1 9 sin b S T 180 ( ) So, TS 9.2 m, S 62, T 54 P DO NOT COPY. Chpter 6: Trigonometry Review Solutions 51

6 10. Two irplnes leve n irport on flight pths tht intersect t n ngle of 50. After one hour, one plne hs trvelled 550 km nd the other hs trvelled 310 km. ) To the nerest kilometre, how fr prt re the plnes? Sketch digrm. Since the given ngle is between the two given sides, only 1 tringle is possible. In ABC, determine BC. 2 b 2 c 2 2bc cos A Substitute: b 310, c 550, A (310)(550) cos (310)(550) cos The plnes re pproximtely 424 km prt. 550 km 50 A 310 km B C b) To the nerest degree, wht is the ngle between the line joining the plnes nd the course of the fster plne? Determine B. sin B sin A b Substitute: A 50, b 310, sin B sin sin 50 sin B Since B is cute: B sin sin b B The ngle between the line joining the plnes nd the course of the fster plne is pproximtely Chpter 6: Trigonometry Review Solutions DO NOT COPY. P

### c The scaffold pole EL is 8 m long. How far does it extend beyond the line JK?

3 7. 7.2 Trigonometry in three dimensions Questions re trgeted t the grdes indicted The digrm shows the ck of truck used to crry scffold poles. L K G m J F C 0.8 m H E 3 m D 6.5 m Use Pythgors Theorem

### SOLVING TRIANGLES USING THE SINE AND COSINE RULES

Mthemtics Revision Guides - Solving Generl Tringles - Sine nd Cosine Rules Pge 1 of 17 M.K. HOME TUITION Mthemtics Revision Guides Level: GCSE Higher Tier SOLVING TRIANGLES USING THE SINE AND COSINE RULES

### INTRODUCTION TO TRIGONOMETRY AND ITS APPLICATIONS

CHAPTER 8 INTRODUCTION TO TRIGONOMETRY AND ITS APPLICATIONS (A) Min Concepts nd Results Trigonometric Rtios of the ngle A in tringle ABC right ngled t B re defined s: sine of A = sin A = side opposite

### REVIEW QUESTIONS TOPIC 5 TRIGONOMETRY I FLUENCY

TOPIC 5 TRIGONOMETRY I REVIEW QUESTIONS FLUENCY The most urte mesure for the length of the third side in the tringle elow is: A 4.83 m B 23.3 m C 3.94 m D 2330 mm E 4826 mm 2 Wht is the vlue of x in this

### TRIGONOMETRIC APPLICATIONS

HPTER TRIGONOMETRI PPLITIONS n ocen is vst expnse tt cn e life-tretening to person wo experiences disster wile oting. In order for elp to rrive on time, it is necessry tt te cost gurd or sip in te re e

### Polar Coordinates. July 30, 2014

Polr Coordintes July 3, 4 Sometimes it is more helpful to look t point in the xy-plne not in terms of how fr it is horizontlly nd verticlly (this would men looking t the Crtesin, or rectngulr, coordintes

### (1) Primary Trigonometric Ratios (SOH CAH TOA): Given a right triangle OPQ with acute angle, we have the following trig ratios: ADJ

Tringles nd Trigonometry Prepred y: S diyy Hendrikson Nme: Dte: Suppose we were sked to solve the following tringles: Notie tht eh tringle hs missing informtion, whih inludes side lengths nd ngles. When

### 1 tray of toffee 1 bar of toffee. 10 In the decimal number, 0 7, the 7 refers to 7 tenths or

Chpter 3 Deciml Numers Do you know wht DECIMAL is? In chpter, we delt with units, s, 0 s nd 00 s. When you tke single unit nd divide it into (or 0 or 00) its, wht we then hve re deciml frctions of whole

### Section 10.2 Graphing Polar Equations

Section 10.2 Grphing Polr Equtions OBJECTIVE 1: Sketching Equtions of the Form rcos, rsin, r cos r sin c nd Grphs of Polr Equtions of the Form rcos, rsin, r cos r sin c, nd where,, nd c re constnts. The

### Skills Practice Skills Practice for Lesson 4.1

Skills Prctice Skills Prctice for Lesson.1 Nme Dte Tiling Bthroom Wll Simplifying Squre Root Expressions Vocbulry Mtch ech definition to its corresponding term. 1. n expression tht involves root. rdicnd

### Section 6.1 Law of Sines. Notes. Oblique Triangles - triangles that have no right angles. A c. A is acute. A is obtuse

Setion 6.1 Lw of Sines Notes. Olique Tringles - tringles tht hve no right ngles h is ute h is otuse Lw of Sines - If is tringle with sides,, nd, then sin = sin = sin or sin = sin = sin The miguous se (SS)

### 9.4. ; 65. A family of curves has polar equations. ; 66. The astronomer Giovanni Cassini ( ) studied the family of curves with polar equations

54 CHAPTER 9 PARAMETRIC EQUATINS AND PLAR CRDINATES 49. r, 5. r sin 3, 5 54 Find the points on the given curve where the tngent line is horizontl or verticl. 5. r 3 cos 5. r e 53. r cos 54. r sin 55. Show

### Yellowknife km Vancouver km NEL

ic tio n Yellowknife Pr e- Pu bl 1566 km 67.3 Vncouver 112 1870 km hpter 3 tio n cute Tringle Trigonometry ic LERNING GOLS You will be ble to develop your sptil sense by Pr e- Pu bl? Using the sine lw

### Geometric quantities for polar curves

Roerto s Notes on Integrl Clculus Chpter 5: Bsic pplictions of integrtion Section 10 Geometric quntities for polr curves Wht you need to know lredy: How to use integrls to compute res nd lengths of regions

### Translate and Classify Conic Sections

TEKS 9.6 A.5.A, A.5.B, A.5.D, A.5.E Trnslte nd Clssif Conic Sections Before You grphed nd wrote equtions of conic sections. Now You will trnslte conic sections. Wh? So ou cn model motion, s in E. 49. Ke

### METHOD OF LOCATION USING SIGNALS OF UNKNOWN ORIGIN. Inventor: Brian L. Baskin

METHOD OF LOCATION USING SIGNALS OF UNKNOWN ORIGIN Inventor: Brin L. Bskin 1 ABSTRACT The present invention encompsses method of loction comprising: using plurlity of signl trnsceivers to receive one or

### Electronic Circuits I - Tutorial 03 Diode Applications I

Electronic Circuits I - Tutoril 03 Diode Applictions I -1 / 9 - T & F # Question 1 A diode cn conduct current in two directions with equl ese. F 2 When reverse-bised, diode idelly ppers s short. F 3 A

### 10.4 AREAS AND LENGTHS IN POLAR COORDINATES

65 CHAPTER PARAMETRIC EQUATINS AND PLAR CRDINATES.4 AREAS AND LENGTHS IN PLAR CRDINATES In this section we develop the formul for the re of region whose oundry is given y polr eqution. We need to use the

### Exercise 1-1. The Sine Wave EXERCISE OBJECTIVE DISCUSSION OUTLINE. Relationship between a rotating phasor and a sine wave DISCUSSION

Exercise 1-1 The Sine Wve EXERCISE OBJECTIVE When you hve completed this exercise, you will be fmilir with the notion of sine wve nd how it cn be expressed s phsor rotting round the center of circle. You

### Study Guide # Vectors in R 2 and R 3. (a) v = a, b, c = a i + b j + c k; vector addition and subtraction geometrically using parallelograms

Study Guide # 1 MA 26100 - Fll 2018 1. Vectors in R 2 nd R 3 () v =, b, c = i + b j + c k; vector ddition nd subtrction geometriclly using prllelogrms spnned by u nd v; length or mgnitude of v =, b, c,

### Section 16.3 Double Integrals over General Regions

Section 6.3 Double Integrls over Generl egions Not ever region is rectngle In the lst two sections we considered the problem of integrting function of two vribles over rectngle. This sitution however is

### Spiral Tilings with C-curves

Spirl Tilings with -curves Using ombintorics to Augment Trdition hris K. Plmer 19 North Albny Avenue hicgo, Illinois, 0 chris@shdowfolds.com www.shdowfolds.com Abstrct Spirl tilings used by rtisns through

### FP2 POLAR COORDINATES: PAST QUESTIONS

FP POLAR COORDINATES: PAST QUESTIONS. The curve C hs polr eqution r = cosθ, () Sketch the curve C. () (b) Find the polr coordintes of the points where tngents to C re prllel to the initil line. (6) (c)

### University of North Carolina-Charlotte Department of Electrical and Computer Engineering ECGR 4143/5195 Electrical Machinery Fall 2009

Problem 1: Using DC Mchine University o North Crolin-Chrlotte Deprtment o Electricl nd Computer Engineering ECGR 4143/5195 Electricl Mchinery Fll 2009 Problem Set 4 Due: Thursdy October 8 Suggested Reding:

### Example. Check that the Jacobian of the transformation to spherical coordinates is

lss, given on Feb 3, 2, for Mth 3, Winter 2 Recll tht the fctor which ppers in chnge of vrible formul when integrting is the Jcobin, which is the determinnt of mtrix of first order prtil derivtives. Exmple.

### Polar coordinates 5C. 1 a. a 4. π = 0 (0) is a circle centre, 0. and radius. The area of the semicircle is π =. π a

Polr coordintes 5C r cos Are cos d (cos + ) sin + () + 8 cos cos r cos is circle centre, nd rdius. The re of the semicircle is. 8 Person Eduction Ltd 8. Copying permitted for purchsing institution only.

### Lecture 20. Intro to line integrals. Dan Nichols MATH 233, Spring 2018 University of Massachusetts.

Lecture 2 Intro to line integrls Dn Nichols nichols@mth.umss.edu MATH 233, Spring 218 University of Msschusetts April 12, 218 (2) onservtive vector fields We wnt to determine if F P (x, y), Q(x, y) is

### First Round Solutions Grades 4, 5, and 6

First Round Solutions Grdes 4, 5, nd 1) There re four bsic rectngles not mde up of smller ones There re three more rectngles mde up of two smller ones ech, two rectngles mde up of three smller ones ech,

### Theme: Don t get mad. Learn mod.

FERURY When 1 is divided by 5, the reminder is. nother wy to sy this is opyright 015 The Ntionl ouncil of Techers of Mthemtics, Inc. www.nctm.org. ll rights reserved. This mteril my not be copied or distributed

### Chapter 11 Trigonometric Ratios The Sine Ratio

Chapter 11 Trigonometric Ratios 11.2 The Sine Ratio Introduction The figure below shows a right-angled triangle ABC, where B = and C = 90. A hypotenuse B θ adjacent side of opposite side of C AB is called

### Synchronous Machine Parameter Measurement

Synchronous Mchine Prmeter Mesurement 1 Synchronous Mchine Prmeter Mesurement Introduction Wound field synchronous mchines re mostly used for power genertion but lso re well suited for motor pplictions

### Synchronous Machine Parameter Measurement

Synchronous Mchine Prmeter Mesurement 1 Synchronous Mchine Prmeter Mesurement Introduction Wound field synchronous mchines re mostly used for power genertion but lso re well suited for motor pplictions

### Synchronous Generator Line Synchronization

Synchronous Genertor Line Synchroniztion 1 Synchronous Genertor Line Synchroniztion Introduction One issue in power genertion is synchronous genertor strting. Typiclly, synchronous genertor is connected

### Using Trigonometric Ratios Part 1: Solving For Unknown Sides

MPM2D: Principles of Mathematics Using Trigonometric Ratios Part 1: Solving For Unknown Sides J. Garvin Slide 1/15 Recap State the three primary trigonometric ratios for A in ABC. Slide 2/15 Recap State

### Student Book SERIES. Patterns and Algebra. Name

E Student Book 3 + 7 5 + 5 Nme Contents Series E Topic Ptterns nd functions (pp. ) identifying nd creting ptterns skip counting completing nd descriing ptterns predicting repeting ptterns predicting growing

### Misty. Sudnow Dot Songs

Sudnow Dot Songs isty T The Dot Song is nottionl system tht depicts voiced chords in wy where the non-music reder cn find these firly redily. But the Dot Song is not intended be red, not s sight reder

### Section 17.2: Line Integrals. 1 Objectives. 2 Assignments. 3 Maple Commands. 1. Compute line integrals in IR 2 and IR Read Section 17.

Section 7.: Line Integrls Objectives. ompute line integrls in IR nd IR 3. Assignments. Red Section 7.. Problems:,5,9,,3,7,,4 3. hllenge: 6,3,37 4. Red Section 7.3 3 Mple ommnds Mple cn ctully evlute line

### 6.2 Slopes of Parallel and Perpendicular Lines

. Slopes of Parallel and Perpendicular Lines FOCUS Use slope to find out if two lines are parallel or perpendicular. These two lines are parallel. Slope of line AB Slope of line CD These two lines have

### Notes on Spherical Triangles

Notes on Spheril Tringles In order to undertke lultions on the elestil sphere, whether for the purposes of stronomy, nvigtion or designing sundils, some understnding of spheril tringles is essentil. The

### Algebra Practice. Dr. Barbara Sandall, Ed.D., and Travis Olson, M.S.

By Dr. Brr Sndll, Ed.D., Dr. Melfried Olson, Ed.D., nd Trvis Olson, M.S. COPYRIGHT 2006 Mrk Twin Medi, Inc. ISBN 978-1-58037-754-6 Printing No. 404042-EB Mrk Twin Medi, Inc., Pulishers Distriuted y Crson-Dellos

### Chapter 5 Analytic Trigonometry

Section 5. Fundmentl Identities 03 Chter 5 Anlytic Trigonometry Section 5. Fundmentl Identities Exlortion. cos / sec, sec / cos, nd tn sin / cos. sin / csc nd tn / cot 3. csc / sin, cot / tn, nd cot cos

### Scale drawing / loci / symmetry 1

1) The scale on a map is 1 : 20 000. Calculate the actual distance between two points which are 2.7 cm apart on the map. Give your answer in kilometres. nswer km [2] 2) C (a) On the diagram above, using

### (a) Construct triangle ABC accurately, with AC = 10 cm and BC = 8 cm. The line AB has been drawn for you. [2]

8 (a) Construct triangle C accurately, with C = 10 cm and C = 8 cm. The line has been drawn for you. [2] (b) (i) Using a straight edge and compasses only, construct the bisector of angle. [2] (ii) The

### Chapter 5 Analytic Trigonometry

Section 5. Fundmentl Identities 03 Chter 5 Anlytic Trigonometry Section 5. Fundmentl Identities Exlortion. cos > sec, sec > cos, nd tn sin > cos. sin > csc nd tn > cot 3. csc > sin, cot > tn, nd cot cos

### Seven Sisters. Visit for video tutorials

Seven Sisters This imge is from www.quiltstudy.org. Plese visit this website for more informtion on Seven Sisters quilt ptterns. Visit www.blocloc.com for video tutorils 1 The Seven Sisters design cn be

### CHAPTER 2 LITERATURE STUDY

CHAPTER LITERATURE STUDY. Introduction Multipliction involves two bsic opertions: the genertion of the prtil products nd their ccumultion. Therefore, there re two possible wys to speed up the multipliction:

### Module 9. DC Machines. Version 2 EE IIT, Kharagpur

Module 9 DC Mchines Version EE IIT, Khrgpur esson 40 osses, Efficiency nd Testing of D.C. Mchines Version EE IIT, Khrgpur Contents 40 osses, efficiency nd testing of D.C. mchines (esson-40) 4 40.1 Gols

### Kirchhoff s Rules. Kirchhoff s Laws. Kirchhoff s Rules. Kirchhoff s Laws. Practice. Understanding SPH4UW. Kirchhoff s Voltage Rule (KVR):

SPH4UW Kirchhoff s ules Kirchhoff s oltge ule (K): Sum of voltge drops round loop is zero. Kirchhoff s Lws Kirchhoff s Current ule (KC): Current going in equls current coming out. Kirchhoff s ules etween

### Book 2. The wee Maths Book. Growth. Grow your brain. N4 Relationships. of Big Brain

Grow your brain N4 Relationships Book 2 Guaranteed to make your brain grow, just add some effort and hard work Don t be afraid if you don t know how to do it, yet! The wee Maths Book of Big Brain Growth

### Domination and Independence on Square Chessboard

Engineering nd Technology Journl Vol. 5, Prt, No. 1, 017 A.A. Omrn Deprtment of Mthemtics, College of Eduction for Pure Science, University of bylon, bylon, Irq pure.hmed.omrn@uobby lon.edu.iq Domintion

### 8.1. The Sine Law. Investigate. Tools

8.1 Te Sine Lw Mimi 50 ermud Tringle ermud 1600 km Sn Jun 74 Puerto Rio Te ermud Tringle, in te nort tlnti Oen, is te lotion of severl unexplined plne nd sip disppernes. Vrious teories ve een suggested

### + sin bsin. sin. tan

6. Spheril rignmetri Frmule Just s in plne gemetry, there re useful trignmetri frmule whih relte the sides nd vertex ngles f spheril tringles: Csine Frmul [6.1] s ss + sin sin s Sine Frmul [6.] sin sin

### SAMPLE. End of term: TEST A. Year 4. Name Class Date. Complete the missing numbers in the sequences below.

End of term: TEST A You will need penil nd ruler. Yer Nme Clss Dte 2 Complete the missing numers in the sequenes elow. 50 25 00 75 8 30 3 28 2 9 Put irle round two of the shpes elow whih hve 3 shded. 3

### Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world

Person Edution Limited Edinurgh Gte Hrlow Essex M20 2JE Englnd nd ssoited ompnies throughout the world Visit us on the World Wide We t: www.personed.o.uk Person Edution Limited 2014 ll rights reserved.

### Book 17. The wee Maths Book. Growth. Grow your brain. Green. of Big Brain. Guaranteed to make your brain grow, just add some effort and hard work

Grow your brain Green Book 17 Guaranteed to make your brain grow, just add some effort and hard work Don t be afraid if you don t know how to do it, yet! The wee Maths Book of Big Brain Growth Enlargement

### MEASURE THE CHARACTERISTIC CURVES RELEVANT TO AN NPN TRANSISTOR

Electricity Electronics Bipolr Trnsistors MEASURE THE HARATERISTI URVES RELEVANT TO AN NPN TRANSISTOR Mesure the input chrcteristic, i.e. the bse current IB s function of the bse emitter voltge UBE. Mesure

### & Y Connected resistors, Light emitting diode.

& Y Connected resistors, Light emitting diode. Experiment # 02 Ojectives: To get some hndson experience with the physicl instruments. To investigte the equivlent resistors, nd Y connected resistors, nd

### ABB STOTZ-KONTAKT. ABB i-bus EIB Current Module SM/S Intelligent Installation Systems. User Manual SM/S In = 16 A AC Un = 230 V AC

User Mnul ntelligent nstlltion Systems A B 1 2 3 4 5 6 7 8 30 ma 30 ma n = AC Un = 230 V AC 30 ma 9 10 11 12 C ABB STOTZ-KONTAKT Appliction Softwre Current Vlue Threshold/1 Contents Pge 1 Device Chrcteristics...

### NONCLASSICAL CONSTRUCTIONS II

NONLSSIL ONSTRUTIONS II hristopher Ohrt UL Mthcircle - Nov. 22, 2015 Now we will try ourselves on oncelet-steiner constructions. You cn only use n (unmrked) stright-edge but you cn ssume tht somewhere

### Alternating-Current Circuits

chpter 33 Alternting-Current Circuits 33.1 AC Sources 33.2 esistors in n AC Circuit 33.3 Inductors in n AC Circuit 33.4 Cpcitors in n AC Circuit 33.5 The LC Series Circuit 33.6 Power in n AC Circuit 33.7

### Question 1 TELE4353. Question 1, cnt d. What is CDMA? Direct Sequence Spread Spectrum System Model. What is direct sequence CDMA?

TELE45 Mobie nd Steite Couniction Systes Tutori 5 week - S 4 Question A ceur obie couniction syste is using direct sequence code diision utipe ccess CDMA technique with coherent binry phse shift keying

### Three-Phase Synchronous Machines The synchronous machine can be used to operate as: 1. Synchronous motors 2. Synchronous generators (Alternator)

Three-Phse Synchronous Mchines The synchronous mchine cn be used to operte s: 1. Synchronous motors 2. Synchronous genertors (Alterntor) Synchronous genertor is lso referred to s lterntor since it genertes

### Vocabulary Check. Section 10.8 Graphs of Polar Equations not collinear The points are collinear.

Section.8 Grphs of Polr Equtions 98 9. Points:,,,,.,... The points re colliner. 9. Points:.,,.,,.,... not colliner. Section.8 Grphs of Polr Equtions When grphing polr equtions:. Test for symmetry. () )

Spheril Geometry This is n rtile from my home pge: www.olewitthnsen.dk Ole Witt-Hnsen nov. 6 Contents. Geometry on sphere.... Spheril tringles...3. Polr tringles...4 3. The right-ngle spheril tringle...6

### CS 135: Computer Architecture I. Boolean Algebra. Basic Logic Gates

Bsic Logic Gtes : Computer Architecture I Boolen Algebr Instructor: Prof. Bhgi Nrhri Dept. of Computer Science Course URL: www.ses.gwu.edu/~bhgiweb/cs35/ Digitl Logic Circuits We sw how we cn build the

### Two-layer slotted-waveguide antenna array with broad reflection/gain bandwidth at millimetre-wave frequencies

Two-lyer slotted-wveguide ntenn rry with rod reflection/gin ndwidth t millimetre-wve frequencies S.-S. Oh, J.-W. Lee, M.-S. Song nd Y.-S. Kim Astrct: A 24 24 slotted-wveguide rry ntenn is presented in

### ECE 274 Digital Logic. Digital Design. Datapath Components Shifters, Comparators, Counters, Multipliers Digital Design

ECE 27 Digitl Logic Shifters, Comprtors, Counters, Multipliers Digitl Design..7 Digitl Design Chpter : Slides to ccompny the textbook Digitl Design, First Edition, by Frnk Vhid, John Wiley nd Sons Publishers,

### Experiment 3: Non-Ideal Operational Amplifiers

Experiment 3: Non-Idel Opertionl Amplifiers Fll 2009 Equivlent Circuits The bsic ssumptions for n idel opertionl mplifier re n infinite differentil gin ( d ), n infinite input resistnce (R i ), zero output

### (CATALYST GROUP) B"sic Electric"l Engineering

(CATALYST GROUP) B"sic Electric"l Engineering 1. Kirchhoff s current l"w st"tes th"t (") net current flow "t the junction is positive (b) Hebr"ic sum of the currents meeting "t the junction is zero (c)

### Regular languages can be expressed as regular expressions.

Regulr lnguges cn e expressed s regulr expressions. A generl nondeterministic finite utomton (GNFA) is kind of NFA such tht: There is unique strt stte nd is unique ccept stte. Every pir of nodes re connected

### Proposed Cable Tables for SAS2

Tle 50 Requirements for internl le ssemlies using SASDrive onnetors n kplnes. Requirement, Units 1,5 Gps 3Gps 6 Gps Bulk le or kplne:, Differentil impene ohm 100 ± 10 100 g Common-moe impene ohm 32,5 ±

### UNDERSTAND SIMILARITY IN TERMS OF SIMILARITY TRANSFORMATIONS

UNDERSTAND SIMILARITY IN TERMS OF SIMILARITY TRANSFORMATIONS KEY IDEAS 1. A dilation is a transformation that makes a figure larger or smaller than the original figure based on a ratio given by a scale

### Year 10 Term 1 Homework

Yimin Math Centre Year 10 Term 1 Homework Student Name: Grade: Date: Score: Table of contents 6 Year 10 Term 1 Week 6 Homework 1 6.1 Triangle trigonometry................................... 1 6.1.1 The

### Indoor Autonomous Vehicle Navigation A Feasibility Study Based on Infrared Technology

Concept Pper Indoor utonomous Vehicle Nvigtion Fesibility Study Bsed on Infrred Technology Ry-Shine Run Zhi-Yu Xio * ID Deprtment Electronics Engineering, Ntionl United University, 36003 Mioli, Tiwn; rsrun@nuu.edu.tw

### Trigonometric ratios 9B 1 a d b 2 a c b

Trigonometric ratios 9B 1 a a Using sin A sin B 8 sin 72 sin 30 8sin 72 sin 30 As 72 > 30, > 8 cm 15.2 cm ( ) ABC 180 68.4 + 83.7 27.9 Using a 9.8 sin 27.9 sin 83.7 9.8sin 27.9 a sin 83.7 4.61 cm ( ) 2

### Chapter 2: Pythagoras Theorem and Trigonometry (Revision)

Chapter 2: Pythagoras Theorem and Trigonometry (Revision) Paper 1 & 2B 2A 3.1.3 Triangles Understand a proof of Pythagoras Theorem. Understand the converse of Pythagoras Theorem. Use Pythagoras 3.1.3 Triangles

### Analytical geometry. Multiple choice questions

Analytical geometry Multiple choice questions 1. Temperature readings on any given day in Québec can vary greatly. The temperatures for a fall day in Montreal were recorded over a 10-hour interval. The

### b = and their properties: b 1 b 2 b 3 a b is perpendicular to both a and 1 b = x = x 0 + at y = y 0 + bt z = z 0 + ct ; y = y 0 )

***************** Disclimer ***************** This represents very brief outline of most of the topics covered MA261 *************************************************** I. Vectors, Lines nd Plnes 1. Vector

### Experiment 8 Series DC Motor (II)

Ojectives To control the speed of loded series dc motor y chnging rmture voltge. To control the speed of loded series dc motor y dding resistnce in prllel with the rmture circuit. To control the speed

### Math 116 Calculus II

Mth 6 Clculus II Contents 7 Additionl topics in Integrtion 7. Integrtion by prts..................................... 7.4 Numericl Integrtion.................................... 7 7.5 Improper Integrl......................................

### CHAPTER 3 AMPLIFIER DESIGN TECHNIQUES

CHAPTER 3 AMPLIFIER DEIGN TECHNIQUE 3.0 Introduction olid-stte microwve mplifiers ply n importnt role in communiction where it hs different pplictions, including low noise, high gin, nd high power mplifiers.

### Dumfries and Galloway Council. Relationships Revision. Mathematics. Suzanne Stoppard. National 4

Dumfries and Galloway Council Relationships Revision Mathematics Suzanne Stoppard National 4 Self Assessment Summary- 1.1 Applying algebraic skills to linear equations Assessment standard Traffic Lights

### Patterns and Algebra

Student Book Series D Mthletis Instnt Workooks Copyright Series D Contents Topi Ptterns nd funtions identifying nd reting ptterns skip ounting ompleting nd desriing ptterns numer ptterns in tles growing

### Crime Scene Documentation. Crime Scene Documentation. Taking the C.S. What should my notes include. Note Taking 9/26/2013

Crime Scene Documenttion Crime Scene Documenttion Most importnt step in C.S. processing Purpose: permnently record the condition of C.S. & physicl evidence Time consuming Documenter must be orgnized nd

### Experiment 3: Non-Ideal Operational Amplifiers

Experiment 3: Non-Idel Opertionl Amplifiers 9/11/06 Equivlent Circuits The bsic ssumptions for n idel opertionl mplifier re n infinite differentil gin ( d ), n infinite input resistnce (R i ), zero output

### Performance Comparison between Network Coding in Space and Routing in Space

Performnce omprison etween Network oding in Spce nd Routing in Spce Yunqing Ye, Xin Hung, Ting Wen, Jiqing Hung nd lfred Uwitonze eprtment of lectronics nd Informtion ngineering, Huzhong University of

### TIME: 1 hour 30 minutes

UNIVERSITY OF AKRON DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 4400: 34 INTRODUCTION TO COMMUNICATION SYSTEMS - Spring 07 SAMPLE FINAL EXAM TIME: hour 30 minutes INSTRUCTIONS: () Write your nme

### STUDY GUIDE, CALCULUS III, 2017 SPRING

TUY GUIE, ALULU III, 2017 PING ontents hpter 13. Functions of severl vribles 1 13.1. Plnes nd surfces 2 13.2. Grphs nd level curves 2 13.3. Limit of function of two vribles 2 13.4. Prtil derivtives 2 13.5.

### Sequential Logic (2) Synchronous vs Asynchronous Sequential Circuit. Clock Signal. Synchronous Sequential Circuits. FSM Overview 9/10/12

9//2 Sequentil (2) ENGG5 st Semester, 22 Dr. Hden So Deprtment of Electricl nd Electronic Engineering http://www.eee.hku.hk/~engg5 Snchronous vs Asnchronous Sequentil Circuit This Course snchronous Sequentil

### ET 51 EXTERIOR ROOF DRIP SIDE FINISH MOULDING INSTALLATION

EXTERIOR ROOF DRIP SIDE FINISH MOULDING 51 INSTALLATION The procedure descried elow is for the LH side. Use the sme procedure for oth the RH nd LH sides, unless otherwise specified. 1. INSTALL ROOF SIDE

### (1) Non-linear system

Liner vs. non-liner systems in impednce mesurements I INTRODUCTION Electrochemicl Impednce Spectroscopy (EIS) is n interesting tool devoted to the study of liner systems. However, electrochemicl systems

### Lecture 16. Double integrals. Dan Nichols MATH 233, Spring 2018 University of Massachusetts.

Leture 16 Double integrls Dn Nihols nihols@mth.umss.edu MATH 233, Spring 218 University of Msshusetts Mrh 27, 218 (2) iemnn sums for funtions of one vrible Let f(x) on [, b]. We n estimte the re under

### Direct Current Circuits. Chapter Outline Electromotive Force 28.2 Resistors in Series and in Parallel 28.3 Kirchhoff s Rules 28.

P U Z Z L E R If ll these pplinces were operting t one time, circuit reker would proly e tripped, preventing potentilly dngerous sitution. Wht cuses circuit reker to trip when too mny electricl devices

### Investigation of Ground Frequency Characteristics

Journl of Electromgnetic Anlysis nd Applictions, 03, 5, 3-37 http://dx.doi.org/0.436/jem.03.58050 Published Online August 03 (http://www.scirp.org/journl/jem) Mohmed Nyel Electricl Engineering Deprtment,

### stanchion paper roll mandrel base FIGURE P3-12 ramp

1 MCHINE DESIGN - n Integrted pproch stnchion pper ro mndre se FIGURE -1 roem -7 rmp FIGURE -1 roem -8 1-ft grid -0 Run the computer mode CSE for Cse Study (on the CD-ROM in sever nguges) nd move the point

### DESIGN OF CONTINUOUS LAG COMPENSATORS

DESIGN OF CONTINUOUS LAG COMPENSATORS J. Pulusová, L. Körösi, M. Dúbrvská Institute of Robotics nd Cybernetics, Slovk University of Technology, Fculty of Electricl Engineering nd Informtion Technology

### Find all the remaining sides, angles and area of the following triangles

Trigonometry Angles of Elevation and depression 1) If the angle of elevation of the top of a vertical 30m high aerial is 32, how is it to the aerial? 2) From the top of a vertical cliff 80m high the angles

### Safety Relay Unit. Main contacts Auxiliary contact Number of input channels Rated voltage Model Category. possible 24 VAC/VDC G9SA-501.

Sfety Rely Unit The Series Offers Complete Line-up of Compct Units. Four kinds of -mm wide Units re ville: A -pole model, -pole model, nd models with poles nd OFF-dely poles, s well s Two-hnd ler. Simple