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Trigonometry Essentials Practice Workbook with Answers: Master Basic Trig Skills PDF

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Trigonometry Essentials Practice Workbook with Answers Master Basic Trig Skills Improve Your Math Fluency Series ChrisMcMullen,Ph.D. TrigonometryEssentialsPracticeWorkbookwithAnswers: MasterBasicTrigSkills ImproveYourMathFluencySeries Copyright ©2012,2015,2017ChrisMcMullen,Ph.D. All rights reserved. This includes the right to reproduce any portion of this book in any form. However,teacherswhopurchaseonecopyofthisbook,orborrowonephysicalcopy from a library, may make and distribute photocopies of selected pages for instructional purposes for their own classes only. Also, parents who purchase one copy of this book, or borrow one physical copy from a library, may make and distribute photocopiesof selected pagesforusebytheirownchildrenonly. CreateSpace Professional&Technical/Science/Mathematics/Trigonometry Professional&Technical/Education/SpecificSkills/Mathematics/Trigonometry PrinteditionISBN: 1477497781 PrinteditionEAN-13: 978-1477497784 TrigonometryEssentialsPracticeWorkbookwithAnswers Contents MakingtheMostofthisWorkbook 4 Chapter1: ConvertingDegreestoRadians 5 Chapter1Answers 19 Chapter2: ConvertingRadianstoDegrees 21 Chapter2Answers 34 Chapter3: IdentifyingTrigFunctionsinRightTriangles 36 Chapter3Answers 51 Chapter4: SpecialRightTriangles 52 Chapter4Answers 68 Chapter5: MemorizeBasicTrigFunctionsinQuadrantI 69 Chapter5Answers 85 Chapter6: FindingtheReferenceAngle 87 Chapter6Answers 102 Chapter7: DetermineBasicTrigFunctionsinQuadrantsII-IV 104 Chapter7Answers 119 Chapter8: TheInverseTrigFunctions 121 Chapter8Answers 135 Chapter9: TheLawofSinesandtheLawofCosines 137 Chapter9Answers 156 Chapter10: LearnandApplyTrigIdentities 157 Chapter10Answers 180 Chapter11: SolveAlgebraicEquationsthatInvolveTrigFunctions 181 Chapter11Answers 191 3 ImproveYourMathFluencySeries Making the Most of this Workbook  Mathematics is a language. You can’t hold a decent conversation in any language if youhavealimitedvocabularyorifyouarenotfluent. Inordertobecomesuccessful inmathematics,youneed topracticeuntilyouhavemasteredthefundamentalsand developed fluency in the subject. This Trigonometry Essentials Practice Workbook with Answers: Master Basic Trig Skills will helpyou improve the fluency with which you apply fundamental trig techniques. Every problem can be answered without a calculator, which isvery helpful for studentswho aren’t allowed to use a calculator. This is the case in some trig and physics courses, as well as some standardized exams(liketheMCAT).  Thisworkbookisconvenientlydividedinto11chapterssothatyoucanfocusonone basic skill at a time. The first two chapters provide practice converting between degrees and radians. Chapters 3-4 are devoted toward relating the basic trig functions to right triangles; Chapter 4 focuses on the - - and - - triangles. StudentsmasterthebasictrigfunctionsinChapters5-7,andtheirinverse functions in Chapter 8. Chapter 9 is devoted to the law30o°f6si0n°e9s0a°nd law45o°f c4o5s°in9e0s°, and includes several obtuse and acute triangles for practice. Trig identities and their application are the subject of Chapter 10, and Chapter 11 focuses on how to solveequationsthatfeaturetrigfunctions.  Eachchapterbeginswithconciseinstructionsdescribinghowtoperformabasictrig skill – such as how to determine the reference angle. These instructions are followed by a few examples. Use these examplesasa guide untilyoubecome fluent inthetechnique.  After you complete a page, check your answers with the answer key in the back of the book. Practice makes permanent, but not necessarily perfect: If you practice making mistakes, you willlearn yourmistakes. Check your answersand learn from yourmistakes such that youpractice solvingthe problemscorrectly. Thisway your practicewillmakeperfect.  Math can be fun. Make a game of your practice by recording your times and trying to improve on your times, and recordingyour scoresand trying toimprove on your scores. Doing this will help you see how much you are improving, and this sign of improvement can give you the confidence to succeed in math, which can help you learntoenjoythissubjectmore. 4 TrigonometryEssentialsPracticeWorkbookwithAnswers Chapter 1: Converting Degrees to Radians There are two commonmethodsfor measuringangles. One method isto divide a circle up into slices, where each slice equals one degree ( ). In the degree measure, a full circle corresponds to , a right angle is , an equilateral triangle has angles, and so on. Degr3e6es0are very common in science and engineerin°g, since a protractor is typically ruled indegrees. 360° 90° 60° 1° 60° 90° 60° 60° 360° A second method for measuring angles is to work with radians instead of degrees. Radians are defined such that radians correspond to a full circle. The unit radian is often abbreviated rad. In terms of radians, a right angle is rad, an equilateral triangle has angles of rad, and so o2nπ. Radians are very common in math courses since many geometric formulas involve π. π/2 π/3 rad 1 rad π/3 rad rad rad π/3 π/3 π/2 rad 2π Since both unitsfor angular measure – degrees and radians – are very common, it’s usefultobeabletoconvertdegreestoradiansorvice-versa. Themainideabehindtheconversionisgeometric. Forexample, isone-sixthofa circle, since equals . Therefore, the same angle in radiansis rad, since one- sixthof is ,whichreducesto . Similarly, isone-fourthof6a0°circle,since dividedby 6e0q°uals .36T0h°is/6equatesto rad,since dividedby reπd/u3cesto . 2π 2π/6 π/3 90° 360° 4 90° π/2 2π 4 π/2 5 ImproveYourMathFluencySeries Theconversionfactorneededtoconvertdegreestoradiansorvice-versais: radians The reason for this is that a full circl1e8i0s° = πor radians. Therefore, is equivalent to radians. Ifwedividebothquantitiesby ,wefindthat equatesto radians. Dividing both sides by , you can3s6e0e°tha2tπ radian equates to ap3p6r0o°ximately deg2rπees. However,it’susuallymoreconvenien2ttoremember18th0a°t rπadiansthanto memorizethenumber . π 1 57.3 Inthischapter,we willpracticeconvertingdegreesintorad1ia8n0s°.=Thπewaytodothis istomultiplyby radia5n7s.3anddivideby ,asillustratedinthefollowingexamples. Take some time to understand these concepts, and study the examples. Once you understand the fπollowing examples, you1a8r0e°ready to practice the technique yourself. You may need to refer to the examples frequently as you begin, but should try to solve the exercises all by yourself once you get the hang of it. Be sure to check the answers at the backofthebooktoensurethatyouaresolvingtheproblemscorrectly. Instructions: Convertthegivenanglefromdegreestoradians. Procedure: Multiply thegiven angle by and divide by . If the result isa fraction, see if the fraction is reducible. That is, if the numerator and denominator are both evenly divisible by an integer greater than 1, thπen the fraction i1s8r0educible. Reduce a fraction by dividing both the numerator and denominator by the greatest common factor (as in the examplesthatfollow). Example1: rad rad rad 120° Both the numerator ( ) and dπen omina1t2o0r ( ) a2reπ divisible by : , 120°× = π = . Theansweris ra1d8. 0° 180 3 120 180 60 120/60= 2 1E8xa0m/6p0le=23: 2π/3 rad rad rad 30° Both the numerator ( ) and deπn ominat3o0r ( ) aπre divisible by : , 30°× = π = . Theansweris rad1. 80° 180 6 30 180 30 30/30 = 1 1E8xa0m/3p0le=36: π/6 rad rad rad 720° Boththenumerator( )anddenoπm inator7(20 )are divisibleby : . The 720°× = π = 4π answeris rad. 180° 180 720 180 180 720/180 = 4 4π 6 TrigonometryEssentialsPracticeWorkbookwithAnswers Instructions: Convertthegivenanglefromdegreestoradians. Checkyouranswersinthe backofthebook. (1)36° (2)18° (3)780° (4)117° (5)45° (6)12° (7)96° (8)270° (9)120° (10)78° (11)48° (12)150° 7 ImproveYourMathFluencySeries Instructions: Convertthegivenanglefromdegreestoradians. Checkyouranswersinthe backofthebook. (1)210° (2)45° (3)24° (4)3° (5)10° (6)135° (7)96° (8)315° (9)270° (10)42° (11)87° (12)69° 8 TrigonometryEssentialsPracticeWorkbookwithAnswers Instructions: Convertthegivenanglefromdegreestoradians. Checkyouranswersinthe backofthebook. (1)153° (2)48° (3)57° (4)63° (5)96° (6)552° (7)606° (8)132° (9)225° (10)300° (11)129° (12)60° 9 ImproveYourMathFluencySeries Instructions: Convertthegivenanglefromdegreestoradians. Checkyouranswersinthe backofthebook. (1)348° (2)117° (3)105° (4)816° (5)90° (6)57° (7)27° (8)69° (9)525° (10)276° (11)63° (12)636° 10

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