ࡱ> Root Entry  F #|K$WordDocumentHKxL@ԯ(H\}`A`UJ`UJ@ԯ(H\ /ObjectPool@bbPbbb J|J|b(SummaryInformationmmon Files\Microsoft Sha(l32.cnv, html x%j.&'()*+,/0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefgh -klmnopqrstuvwyz{|}~' ( ; < = > ? ^ _ r s t u Y ¹ﱨ~uuD]g7ceKuD]g7avKuD]g7ceKuD]g7avKuD]g7ceKuD]g7avKuD]g7ceKuD]g7avKuD\g7ceKuD\g7avK uD\g7eKuD\g7avKuDuDN\g7ceKuDN\g7avKc uDcuDO\g7ceK.Y Z m n o p        [\opqrxuDI]g7avKuDJ]g7ceKuDJ]g7avKuDK]g7ceKuDK]g7avKuDL]g7ceKuDL]g7avKuDM]g7ceKuDM]g7avKuDN]g7ceKuDN]g7avKuDO]g7ceKuDO]g7avKuDP]g7ceKuDP]g7avKc uDc-bcvwxycdwxyz/012=>QRSTnożﴫxuD]g7ceKuD]g7avKuD]g7ceKuD]g7avKuD]g7ceKuD]g7avKuD]g7ceKuD]g7avKuD]g7ceKuD]g7avKuD]g7ceKuD]g7avKuDk]g7ceKuDk]g7avKc uDcuDI]g7ceK/23FGHIuuD]g7ceKuD]g7avKuD]g7ceKuD]g7avKc uDcuD]g7ceKuD]g7avKhY()?  !h!!F!b!k!]!]!!h!k!!!!!!!!!^ !k!!!:!! !=!x!K@Normala "A@"Default Paragraph Font! EY  8LNr02@TV{=QS';=^rtYmo    [ o q   bvxcwy/1=QSn2FH::::::::::::::::::::::::::::::::::::::::z=BTY7Mary R. Parker,C:\maryo\MATHNRG\webmp\prereqm\trigprobs.docMary R. Parker-C:\maryo\MATHNRG\webmp\prereqm\trigprobs2.docMary R. Parker-C:\maryo\MATHNRG\webmp\prereqm\trigprobs2.docMary R. Parker-C:\maryo\MATHNRG\webmp\prereqm\trigprobs2.docMary R. Parker2C:\maryo\MATHNRG\webmp\prereqm\1753\trigprobs2.doc@HP DeskJet 690C Series PrinterLPT1:HPFDJC05HP DeskJet 690C Series PrinterHP DeskJet 690C Series Printer7d,,HP DeskJet 690C Series PrinterLPT1 ,,HP DeskJet 690C Series Printer7d,,HP DeskJet 690C Series PrinterLPT1 ,,z1Times New Roman Symbol &Arial"qh""!!KFind all solutions in : Mary R. ParkerMary R. ParkerܥhW e/&j&jj&j&j&j&j&&&&&&&(& &.1&)))))))'+)+)+)+Mv+-..XQ/K.j&) )))).)j&j&)&))))Fj&)j&)'+ Ӏ~&&j&j&j&j&)'+)7)1. Give at least two other ways to write the expression EMBED Equation.2 and then find its value. 2. Find all solutions in  EMBED Equation.2 :  EMBED Equation.2  3. Solve  EMBED Equation.2  in the interval  EMBED Equation.2  4. For the following trig function, graph it, including find the amplitude, period, phase shift, and x intercepts:  EMBED Equation.2 . 5. Explain the difference between  EMBED Equation.2  and  EMBED Equation.2 . 6. Find the length of a guy wire that makes an angle of  EMBED Equation.2  with the ground if the wire is attached to the top of a tower 63.0 meters high. 7. Solve the triangle ABC (not a right triangle) if A EMBED Equation.2 , b=12.9 meters, and c=15.4 meters. 8. Use an appropriate half-angle identity to find the exact value of  EMBED Equation.2 . 9. Prove the following identity:  EMBED Equation.2  Comments and answers: These comments should give enough clues so that you could look up explanations and similar problems in a trig book. 1. Trig functions:  EMBED Equation.2 . The main point here is to notice what the squared means, and the secondary point is to be able to interchange degree and radian measure for angles.  EMBED Equation.2 Root Entry  F #|@T$WordDocumentHKxL@ԯ(H\}`A`UJ`UJ@ԯ(H\s0ObjectPool@bbPbbb J|J|b(SummaryInformationmmon Files\Microsoft Sha(l32.cnv, htmlx"%j.&'()*+,/0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefgh -klmnopqrstuvwyz{|}~!!KFind all solutions in : Mary R. ParkerMary R. Parker  !"#$&*,./012345679=?ABCDEFHMOPQRSUZ\]^_`bgijklmnoqvxyz{|~ܥhW es0?&j&jj&j&j&j&j&&&,&&&&(& &/1')))))))++++M+~-//X(0K6/ij&) ))))6/*j&j&)'***)Fj&)j&)+@T~&&j&j&j&j&)+*y*1. Give at least two other ways to write the expression EMBED Equation.2 and then find its value. 2. Find all solutions in  EMBED Equation.2 :  EMBED Equation.2  3. Solve  EMBED Equation.2  in the interval  EMBED Equation.2  4. For the following trig function, graph it, including find the amplitude, period, phase shift, and x intercepts:  EMBED Equation.2 . 5. Explain the difference between  EMBED Equation.2  and  EMBED Equation.2 . 6. Find the length of a guy wire that makes an angle of  EMBED Equation.2  with the ground if the wire is attached to the top of a tower 63.0 meters high. 7. Solve the triangle ABC (not a right triangle) if A EMBED Equation.2 , b=12.9 meters, and c=15.4 meters. 8. Use an appropriate half-angle identity to find the exact value of  EMBED Equation.2 . 9. Prove the following identity:  EMBED Equation.2  Comments and answers: These comments should give enough clues so that you could look up explanations and similar problems in a trig book. 1. Trig functions:  EMBED Equation.2 . The main point here is to notice what the squared means, and the secondary point is to be able to interchange degree and radian measure for angles.  EMBED Equation.2 . (Actually, most students will be able to do this problem, but may make mistakes when they have variables rather than numbers, perhaps thinking that  EMBED Equation.2 or  EMBED Equation.2 , both of which are incorrect.) 2. Radian measure and circular functions, trig equations:  EMBED Equation.2  3. Trig equations (get 0 on one side, factor, solve the resulting two equations as in number 1 here):  EMBED Equation.2  4. Graphing trig functions (rewrite it as  EMBED Equation.2 i!#): amplitude is 2, the minus in front means it is reflected across the y axis, the period is  EMBED Equation.2 , and the x intercepts are  EMBED Equation.2  to the left of those for the regular cos function, which are  EMBED Equation.2 etc. 5. Inverse trig functions: The first here is the inverse under composition, which is  EMBED Equation.2 . It has domain all real numbers. The second here is  EMBED Equation.2 . It has domain all real numbers except integer multiples of  EMBED Equation.2 . You can further emphasize the difference between the two by evaluating them at several values of x and showing that you get very different values and by graphing them. Notice that the exponent of -1 is not treated like the exponent of 2 in problem number 1 here. The reason is that, for functions, we need a notation for the inverse function under composition, and the first notation here is used for that. For numbers, we dont have the composition operation, so that we can use these two notations interchangeably. In fact, this potential for confusion is part of the reason why we have the different names for the reciprocals for the trig functions, so mathematicians and scientists would not use the notation  EMBED Equation.2 , but would use  EMBED Equation.2  instead. In older books, you would not find the notation  EMBED Equation.2  used nearly as much as  EMBED Equation.2 . However, in newer books, with our increased emphasis on function notation, the notation  EMBED Equation.2 is quite common. All the same considerations apply to the notation for the inverse functions of the other trig functions. 6. Solving right triangles: Sketch a diagram with the guy wire as the hypotenuse of a right triangle, set up an equation with the sin function, and then solve for the unknown value of the hypotenuse. length  EMBED Equation.2  meters 7. Law of Cosines and Law of Sines: Start by finding side a using the law of cosines and we find it to be 10.5 meters. There are several approaches from here. One is to find the law of sines to find one of the other angles. Notice that B must be smaller than angle C, since side b is shorter than side c. Since a triangle cant have two obtuse angles in it, then B, since it is smaller, must be acute. That enables us to avoid any ambiguity in using the law of sines to find B EMBED Equation.2 . Using the fact that the three angles must sum to  EMBED Equation.2 , we find that angle A must be  EMBED Equation.2 . 8. Trig Identities: Express  EMBED Equation.2 as half of  EMBED Equation.2 , use the exact value for  EMBED Equation.2 , and plug this into the half-angle identity for cosine. The answer is  EMBED Equation.2 . 9. Trig identities: Work with the left side, write everything in terms of  EMBED Equation.2 , simplify, rewrite this using a basic identity, turn it into an expression with  EMBED Equation.2  in the denominator, and then rewrite that using a basic identity to get the riEquation Native TCompObjjght-hand side. /=Trigonometry Problems: Trigonometry problem c FMicrosoft Word Document MSWordDocWord.Document.69q՜.+,0HPt|  Austin Community College! Find all solutions in : Oh+'0 ,8 ` l x Find all solutions in : Mary R. Parker Normal.dotMary R. Parker3kMicrosoft Word for Windows 95@G@@XZ@]$lJ0qJmJ cos 2 x FMicrosoft Equation 2.0 DS Equation Equation.29q_929521108'+.FA}A}Ole PIC -0LMETA _929521081*,FF0}8}_929521080@F8}8}_929521079$):F8}A}_9295211094FA}A}_929521039^F3 } '}_929521038&(XF '} '}_929521037RF '}0}_929521082LF0}0}_929520971"vF j} j}_929520970pF j}@ }_929520969!jF@ }@ }_929521003%dF@ }3 }_929520975F@|@|_929520974F@|`B}_929520973 #F`B} j}_929520972|F j} j}_929520916F`|`|_929520915F`|y|_929520914Fy|y|_929520976Fy|@|_929520718F||_929520769F||_929520806F||_929520917F|`|_929518408F|F|_929520721FF|F|_929520720FF||_929520719F||CompObj/2fObjInfo Equation Native 1 @Ole 'PIC 36%LMETA xCompObj58fObjInfoEquation Native 74Ole :PIC 9<8LMETA -CompObj;>+fObjInfo(Equation Native =)LOle IPIC ?BGLMETA @CompObjAD>fObjInfo;Equation Native C<HOle VPIC EHTLMETA NtCompObjGJLfObjInfoJEquation Native IK8Ole cPIC KNaLMETA [tCompObjMPYfObjInfoWEquation Native OX8Ole rPIC QTpLMETA hCompObjSVffObjInfodEquation Native Ue@Ole PIC WZ}LMETA 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CompObjfObjInfoEquation Native Ole PIC LMETA XCompObjfObjInfoEquation Native Ole "PIC  LMETA CompObjfObjInfoEquation Native HOle 2PIC 0LMETA 'CompObj%fObjInfo#Equation Native $@Ole APIC ?LMETA 7CompObj5fObjInfo3Equation Native 4@Ole SPIC QLMETA G|CompObjEfObjInfoBEquation Native CLOle fPIC dLMETA YCompObjWfObjInfoTEquation Native UPOle xPIC vLMETA l|CompObjjfObjInfogEquation Native hPOle PIC LMETA }CompObj{fObjInfoyEquation Native z8Ole PIC LMETA (CompObj fObjInfoEquation Native  XOle PIC  LMETA CompObj fObjInfoEquation Native POle PIC LMETA CompObjfObjInfoEquation Native 8Ole PIC LMETA CompObjfObjInfo_929516357Fܳ|}|_929517927 F}|}|_929517892F}||_929518048F||  .1   & & MathType Times New Roman- 2 4cos Times New Roman- 2 =2pTimes New Roman- 2 *x & "Systemn-@L,lJ0qJmJ tanx FMicrosoft Equation 2.0 DS Equation Equation.29q  .1  `& ` & MathType Times New Roman|- 2 @@tankTimes New Romany- 2 @[x & "Systemn-L0lJ0qJmJ  2+ 3  2 FMicrosoft Equation 2.0 DS Equation Equation.29qz A .1  &6 & MathType "-  "--{{Gh-:-:RFRFRg@Times New Romanx- 2 X2 2 3 2 (2Symbol- 2 g+ & "Systemn-Lz,lJ0qJmJ cos(30 0 ) FMicrosoft Equation 2.0 DS Equation Equation.29qV{  .1  @& & MathTypePTimes New Roman- 2 4cos(~ 2 )~ 2 30 Times New Roman- 2 L0p & "Systemn-LV{hlJ0qJmJ 30 0 FMicrosoft Equation 2.0 DS Equation Equation.29q  .1  &@ & MathType Times New Roman- 2 430 Times New Roman!- 2 0p & "Systemn-L,lJ0qJmJ 15 0 FMicrosoft Equation 2.0 DS Equation Equation.29q  .1  `&  & MathType Times New Roman!- 2 15 Times New Roman5- 2 0p & "Systemn-L|,$lJ0qJmJ 81.9 0 FMicrosoft Equation 2.0 DS Equation Equation.29q  .1  `&  & MathType Times New Roman- 2 (81 2 9 Times New Roman- 2 0pTimes New Roman- 2 ~.` & "Systemn-L, lJ0qJmJ 180 0 FMicrosoft Equation 2.0 DS Equation Equation.29qq  .1   & & MathType Times New Romany- 2 180 Times New Roman- 2 m0p & "Systemn-Lq,$lJ0qJmJ =55.8 0 FMicrosoft Equation 2.0 DS Equation Equation.29q  .1  &` & MathType Symbol- 2 <=Times New Roman- 2 j55 2 8 Times New Roman- 2 0pTimes New Roman- 2 .` & "Systemn-GL,XlJ0qJmJ =63.0sin(52.5 o )=79.4 FMicrosoft Equation 2.0 DS Equation Equation.29q:  O .1    &  & MathType "-Symbol- 2 <= 2  =Times New Roman4- 2 j[63 2 j 0 2 5 2 F 79 2  4 2 j.`2 sin(52k~ 2 N.` 2 )~ 2  .` Times New Roman- 2 Uop & "Systemn-LL: 4lJ0qJmJ f(x)=tan -1 x FMicrosoft Equation 2.0 DS Equation Equation.29q { C .1  @ & & MathTypePTimes New Roman- 2 {fk 2 x 2 xTimes New Roman- 2 K(~ 2 )~ 2 tankSymbol- 2 = Symbol- 2 -{ Times New Roman- 2 G1p & "Systemn-0L {h0lJ0qJmJ f(x)=arct_929515074F||_929515147 F|പ|_929515507Fപ|ܳ|_929516319 Fܳ|ܳ|anx FMicrosoft Equation 2.0 DS Equation Equation.29q 4  .1   &  & MathTypePTimes New Roman)- 2 `|fk 2 `x 2 `xTimes New Roman- 2 `N(~ 2 `)~2 `arctan~kSymbol- 2 `= & "Systemn-L 4@4lJ0qJmJ f(x)=tan -1 x FMicrosoft Equation 2.0 DS Equation Equation.29q { C .1  @ & & MathTypePTimes New Roman- 2 {fk 2 x 2 xTimes New Roman- 2 K(~ 2 )~ 2 tankSymbol- 2 = Symbol- 2 -{ Times New Roman- 2 G1p & "Systemn-0L {h@lJ0qJmJ g(x)=1tanx=cotx FMicrosoft Equation 2.0 DS Equation Equation.29q E W .1   &@  & MathType "-Times New Roman- 2 Lg 2 x 2 x 2  xTimes New Roman- 2 (~ 2 z)~ 2 tank 2 ] cotkSymbol- 2 f= 2 #=Times New Roman- 2 j1 & "Systemn-L El<lJ0qJmJ g(x)=(tanx) -1 FMicrosoft Equation 2.0 DS Equation Equation.29q { M .1  @ &  & MathTypePTimes New Roman- 2 Lg 2 x 2 9xTimes New Roman- 2 (~ 2 z)~ 2 (tan~k 2 )~Symbol- 2 f= Symbol- 2 -{ Times New Roman- 2  1p & "Systemn-GL {h !#%&'()*+,-./1579:;<=>?@BGIJKLMNPUWXYZ[\^bdfghijklmnopqrtxy{}~ lJ0qJmJ p FMicrosoft Equation 2.0 DS Equation Equation.29q  .1  ``&  & MathType0Symbol- 2 (p & "Systemn-L@lJ0qJmJ g(x)=1tanx=cotx FMicrosoft Equation 2.0 DS Equation Equation.29q E W .1   &@  & MathType "-Times New Romany- 2 Lg 2 x 2 x 2  xTimes New Roman- 2 (~ 2 z)~ 2 tank 2 ] cotkSymbol- 2 f= 2 #=Times New Romany- 2 j1 & "Systemn-L ElTlJ0qJmJ f(x)=tan -1 (x)=arctanx FMicrosoft Equation 2.0 DS Equation Equation.29q{ w .1  @@& & MathTypePTimes New Roman- 2 |fk 2 x 2 x 2 LxTimes New Roman)- 2 N(~ 2 )~ 2 tank 2 (~ 2 = )~2 c arctan~kSymbol- 2 = 2 ) = Symbol- 2 -{ Times New Roman- 2 L1p & "Systemn-L{( h0lJ0qJmJ p6,7p6, FMicrosoft Equation 2.0 DS Equation Equation.29q_E  .1  & & MathType "-@X$Symbol- 2 jHp 2 jpTimes New Roman- 2 r6 2 j87 2 6 2 ,` 2 >,` & "Systemn-L_E llJ0qJmJ p3 FMicrosoft Equation 2.0 DS Equation Equation.29qE  .1  &` & MathType "-@XSymbol- 2 jHpTimes New Roman- 2 x3 & "Systemn-LEllJ0qJmJ 2p3 FMicrosoft Equation 2.0 DS Equation Equation.29qE  .1  `&  & MathType "-@Times New Roman- 2 jT2 2 3Symbol- 2 jp & "Systemn-LE|lTlJ0qJmJ y=-2cos3x+p3()() FMicrosoft Equation 2.0 DS Equation Equation.29q  .1  @&6 & MathType "-<n < Times New Roman:- 2 Xy 2 ; xSymbol- 2 t= 2 - 2 ` 2 @ + 2 j 2 j 2 j 2   2   2   2  2  2  2 F  2 F  2 F Times New Roman:- 2 2 2 3 2  3 2 cosSymbol- 2 v p & "Systemn-LՀlJ0qJmJ {0,p4,p,5p4,2p,9p4,3p,13p4} FMicrosoft Equation 2.0 DS Equation Equation.29qE  .1  & & MathType "-,r,  $Times New Roman- 2 ({ 2 ,` 2 h,` 2 ,` 2 h,` 2 ~ ,` 2 ( ,` 2 &,` 2 } 2 0 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sink Times New Roman!- 2 T2p 2 T0p 2 T 0p 2 T 2p 2 2pTimes New Roman- 2 F30 2 i 30 2 w6Symbol- 2 g= 2 = 2 } 2 } 2 } 2 d 2 d 2 d 2  2  2  2  2  2 Symbol- 2 Jp & "Systemn-L<$հlJ0qJmJ sin 2 (30 0 )=(sin(30 0 )) 2 =12() 2 =14 FMicrosoft Equation 2.0 DS Equation Equation.29qd  .1   &+ & MathType "-\\\\Times New Romany- 2 4sink 2 (~ 2 {)~2 (sin(~k~ 2  ))~~ Times New Roman- 2 42p 2 40p 2 4 0p 2 4 2p 2 2pTimes New Romany- 2 F30 2 i 30 2 1 2 2 2 1 2 4Symbol- 2 g= 2 = 2  2  2  2  2  2  2 = & "Systemn-Ld xlJ0qJmJ tan 2 a(1+cot 2 a)=11-sin     !&()*+,-./1689:;<=>@DFHIJKLMNOPRVXZ[\]^_`abceikmnopqrstuw|~ 2 a FMicrosoft Equation 2.0 DS Equation Equation.29qE  .1  & & MathType "- kTimes New Roman- 2 @tank 2  (~ 2 cotk 2 h )~ 2 sink Times New Roman- 2 02p 2 2p 2 2pTimes New Roman- 2 1 2 j(1 2  1Symbol- 2 a 2 M a 2 BaSymbol- 2 l+ 2 T = 2  - & "Systemn-LE l,lJ0qJmJ cos(15 0 ) FMicrosoft Equation 2.0 DS Equation Equation.29q3{  .1  @&` & MathTypePTimes New Roman|- 2 4cos(~ 2 )~ 2 15 Times New Roman- 2 (0p 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"Systemn-yoL{hDocumentSummaryInformation8_929518792FJ||_929514729F||_929514772 F|| . (Actually, most students will be able to do this problem, but may make mistakes when they have variables rather than numbers, perhaps thinking that  EMBED Equation.2 or  EMBED Equation.2 , both of which are incorrect.) 2. Radian measure and circular functions, trig equations:  EMBED Equation.2  3. Trig equations (get 0 on one side, factor, solve the resulting two equations as in number 1 here):  EMBED Equation.2  4. Graphing trig functions (rewrite it as  EMBED Equation.2 89LMNOrswuDKg7ceKuDKg7avKuDGg7ceKuDGg7avKuDFg7ceKuDFg7acvK uDBFg7eKuDBFg7avKuDuDEg7ceKuDEg7acvKuDDg7ceKuDDg7acvKuDTg7ceKuDTg7avK uDcc-): amplitude is 2, the minus in front means it is reflected across the y axis, the period is  EMBED Equation.2 , and the x intercepts are  EMBED Equation.2  to the left of those for the regular cos function, which are  EMBED Equation.2 etc. 5. Inverse trig functions: The first here is the inverse under composition, which is  EMBED Equation.2 . It has domain all real numbers. The second here is  EMBED Equation.2 . It has domain all real numbers except integer multiples of  EMBED Equation.2 . You can further emphasize the difference between the two by evaluating them at several values of x and showing that you get very different values and by graphing them. Notice that the exponent of -1 is not treated like the exponent of 2 in problem number 1 here. The reason is that, for functions, we need a notation for the inverse function under composition, and the first notation here is used for that. For numbers, we dont have the composition operation, so that we can use these two notations interchangeably. In fact, this potential for confusion is part of the reason why we have the different names for the reciprocals for the trig functions, so mathematicians and scientists would not use the notation  EMBED Equation.2 , but would use  EMBED Equation.2  instead. In older books, you would not find the notation  EMBED Equation.2  used nearly as much as  EMBED Equation.2 . However, in newer books, with our increased emphasis on function notation, the notation  EMBED Equation.2 is quite common. All the same considerations apply to the notation for the inverse functions of the other trig functions. 6. Solving right triangles: Sketch a diagram with the guy wire as the hypotenuse of a right triangle, set up an equation with the sin function, and then solve for the unknown value of the hypotenuse. length  EMBED Equation.2  meters 7. Law of Cosines and Law of Sines: Start by finding side a using the law of cosines and we find it to be 10.5 meters. There are several approaches from here. One is to find the law of sines to find one of the other angles. Notice that B must be smaller than angle C, since side b is shorter than side c. Since a triangle cant have two obtuse angles in it, then B, since it is smaller, must be acute. That enables us to avoid any ambiguity in using the law of sines to find B EMBED Equation.2 . Using the fact that the three angles must sum to  EMBED Equation.2 , we find that angle A must be  EMBED Equation.2 . 8. Trig Identities: Express  EMBED Equation.2 as half of  EMBED Equation.2 , use the exact value for  EMBED Equation.2 , and plug this into the half-angle identity for cosine. The answer is  EMBED Equation.2 . 9. Trig identities: Work with the left side, write everything in terms of  EMBED Equation.2 , simplify, rewrite this using a basic identity, turn it into an expression with  EMBED Equation.2  in the denominator, and then rewrite that using a basic identity to get the right-hand side. /=89LMNOrswuDKg7ceKuDKg7avKuDGg7ceKuDGg7avKuDFg7ceKuDFg7acvK uDBFg7eKuDBFg7avKuDuDEg7ceKuDEg7acvKuDDg7ceKuDDg7acvKuDTg7ceKuDTg7avK uDcc-0123@ATUVW{|=>QRST漳櫢暑所xuDO\g7avKuDP\g7ceKuDP\g7avKuDQ\g7ceKuDQ\g7avKuDHSg7ceKuDHSg7avKuDQg7ceKuDQg7avKuDDQg7ceKuDDQg7avKuDgQg7ceKuDgQg7avKc uDcuDEKg7ceKuDEKg7avK+0123@ATUVW{|=>QRST漳櫢暑所xuDO\g7avKuDP\g7ceKuDP\g7avKuDQ\g7ceKuDQ\g7avKuDHSg7ceKuDHSg7avKuDQg7ceKuDQg7avKuDDQg7ceKuDDQg7avKuDgQg7ceKuDgQg7avKc uDcuDEKg7ceKuDEKg7avK+' ( ; < = > ? ^ _ r s t u Y ¹ﱨ~uuD]g7ceKuD]g7avKuD]g7ceKuD]g7avKuD]g7ceKuD]g7avKuD]g7ceKuD]g7avKuD\g7ceKuD\g7avK uD\g7eKuD\g7avKuDuDN\g7ceKuDN\g7avKc uDcuDO\g7ceK.Y Z m n o p        [\opqrxuDI]g7avKuDJ]g7ceKuDJ]g7avKuDK]g7ceKuDK]g7avKuDL]g7ceKuDL]g7avKuDM]g7ceKuDM]g7avKuDN]g7ceKuDN]g7avKuDO]g7ceKuDO]g7avKuDP]g7ceKuDP]g7avKc uDc-bcvwxycdwxyz/012=>QRSTnożﴫxuD]g7ceKuD]g7avKuD]g7ceKuD]g7avKuD]g7ceKuD]g7avKuD]g7ceKuD]g7avKuD]g7ceKuD]g7avKuD]g7ceKuD]g7avKuDk]g7ceKuDk]g7avKc uDcuDI]g7ceK/23FGHIuuD]g7ceKuD]g7avKuD]g7ceKuD]g7avKc uDcuD]g7ceKuD]g7avKhY()?  !h!!F!b!k!]!]!!h!k!!!!!!!!!^ !k!!!:!! !=!x!!!K@Normala "A@"Default Paragraph Font?! ?E?!!!h!Y  Rfh6JLZnpl02Vjl,.(*+ ? A  % ' 8 L N + ? A ')J^`lauw?::::::::::::::::::::::::::::::::::::::::lqAyMary R. Parker,C:\maryo\MATHNRG\webmp\prereqm\trigprobs.docMary R. Parker-C:\maryo\MATHNRG\webmp\prereqm\trigprobs2.docMary R. Parker-C:\maryo\MATHNRG\webmp\prereqm\trigprobs2.docMary R. Parker-C:\maryo\MATHNRG\webmp\prereqm\trigprobs2.docMary R. Parker2C:\maryo\MATHNRG\webmp\prereqm\1753\trigprobs2.docMary R. Parker2C:\maryo\MATHNRG\webmp\prereqm\1753\trigprobs2.doc@HP DeskJet 690C Series PrinterLPT1:HPFDJC05HP DeskJet 690C Series PrinterHP DeskJet 690C Series Printer7d,,HP DeskJet 690C Series PrinterLPT1 ,,HP DeskJet 690C Series Printer7d,,HP DeskJet 690C Series PrinterLPT1 ,,dPR>?@@AA@8A@@1Times New Roman Symbol &Arial"qh""