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# Class Note for MATH 1330 at UH

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COURSE
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TYPE
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PAGES
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KARMA
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This 6 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 16 views.

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Date Created: 02/06/15
OddNumbered Answers to Exercise Set 44 Trigonometric Expressions and Identities 55 sec8csc8 tan8 00t8 LeftHand Side 50080508 tan800t8 1 I 1 0058 sin8 5in8 0058 0058 sin8 1 0058sin8 sin28 00528 0058sin8 1 0058sin8 0058 sin8 1 sec8csc8 tan800t8 57 tanx7sinxcosx LeftHand Side tanx7sinx005x 5inx 7 005x 7sinx005x sinx7sinx0052x 005x 5inx170052x 005x sinxsin2x 005x tanxsin2x 1 RightHand Side 1 i 1 QED tanxsin2 x RightHand Side tanxsin2 x tanx7sinx005x tanx5inzx Math 1350 Precalculus The Unweisily QfHozstan QED 7 59 cot2 x7cos2 x cot2 x0052 x LeftHand Side RightHand Side 00t2x70052x 00t2x0052x 7 0052x 70052x 7 sin2 x 2 0052 x 7 005 xsin2 x sin2 x 0052x17 sin2 sin2x 0052x0052x 5m2x 00t2x0052x 1 00tzx70052x00tzx0052x QED m csc2 x 75602 x 61 Sinxcosx LeftHand Side sinx005x RightHand Side 0502x75002 x 0052x751n2x 0052x sin2x sin2 x0052x 7 sin2 x0052 x 1 1 7 sin2 x 0052 x 0502 x 7 5002 x 00tx7tanx sinxcosx csc misec x QED Seiunons to Chapter 4 Exercises OddNumbered Answers to Exercise Set 44 Trigonometric Expressions and Identities 7 63 2cos2 x55in2 x 23sin2 x LeftHand Side RightHand Side Zoos2x Ssin2x 23sin2 x 20052x 25in2x3sin2x 20052x sin2x3sin2x 213sin2x 2 35in2 x 2cos2 x55in2 x 23sin2 x QED 7 65 tan4 6tan2 6 sec4 67sec2 6 LeftHand Side RightHand Side tan46tan26 580467se028 tan29tan291 tan2 85802 6 sec2 81SSCZ 6 58048SSC28 tan4 6tan2 6 sec4 67sec2 6 QED Math 1350 Precalculus The Unzversmr QfHozston 67 Two methods of proof are shown Either method is sufficient Method 1 Work with the lefthand side and show that it is equal to the righthand side sinx 7 7 t 1cosx cscx co x LeftHand Side RightHand Side sinx cscx7cotx sinx 17 cosx 1 cosx 17 cosx sinxlicosx licoszx sinxlicosx sin2 x 17 cosx sinx 1 icosx sinx sinx cscx7 cotx sinx cscltxgticotx QED Continued on the nextpage Samursz to Chapter 4 Exercises OddNumbered Answers to Exercise Set 44 Trigonometric Expressions and Identities Method 2 Work with the righthand side and show that it is equal to the lefthand side sufficient 69 Two methods of proof are shown Either method is sinx cscltxgticotltxgt Method Work with the lefthand side and show 1 cosx that it is equal to the righthand side cosx 7 lisinx LeftHand Side RightHand Side s1n x cos x sinx cscx7cotx mm 7 1 7 005m LeftHand Side RightHand Side isinx sinx cosx lisinx 717005 1sinx cosx 7 sinx 7 cosx Ilisinx ipicosw 1COSX lsinx lisinx 7 sinx I1cosx icosxlisinx 739 2 7 170052 1 Sin x 7 sinx1 cosx 7 cosxlisinx 7 sin2x cos x 7 sinx1 cosx lisinx Sinx cosx 1 cosx cosx 7 lisinx QED 39 1sinx 7 cosx quot Lxcscx7cotx QED 39 1cosx Continued on the nexlpage Math 1350 Precalculus The Unzvemmr of Houston Solutions to Chapter 4 Exercises OddNumbered Answers to Exercise Set 44 Trigonometric Expressions and Identities Method 2 Work with the righthand side and show 73 that it is equal to the lefthand side cosx 1isinx 1sinx cosx LeftHand Side RightHand Side 55 cosx lisinx 1 sinx cosh 1 7 smx 1 smx Note The Iriangle may not be drawn to scale cosx 1 sinx 2 3J3 7J3 175m x sm6T 3546 7 cosx1 sinx 2 C052 cos6 7 cosx1 sinx 3 5 2 5 7 cosx tan67T cot67 7 1sinx cosx lisinx ED 1sinx cosx Q 7539 71 k Note The ung may301 b drawn to scale si 677E csc6 Q 29 2 Note T111 triangle may noi be drawn lo scale co 677 sec67E 29 5 csc6 4 cot6 0056 g sec6 5 13 77 sin6 7 csc6 7 B 13 5 tan6 cot67E 12 13 15 cos67 sec67 13 12 75 12 t 6 t 6 7 7 an 12 co 5 Math 1 50 Precalculus The Univeiis v QfHous tan Solutions to Chapter 4 Exercises OddNumbered Answers to Exercise Set 44 Trigonometric Expressions and Identities 79 sin67W csc67 cos67 5606 10 3 1 tan6 cot63 Math 1350 Pvecalculus The Univemzly QfHouston Solutions to Chapter 4 Exercises OddNumbered Answers to Exercise Set 44 Trigonometric Expressions and Identities 11 13 15 17 19 21 23 25 cos2 6sin2 6 1 26 3926 cossm 1 cos2 6 cos2 6 7 cos2 6 1tan2 6 sec2 6 sm67 n67 csc6 79 cos677 677 tan6 cot64J cot6 7 7 sin6 7 7 csc6 sin6 g sin67 csc67 cos67 sec67 cot6 sin2625in6715 csc2 x76cscx9 3sin677cos6 cos6sin6 73tan6sin6 5 sin67cos6 Ssin677cos6 sec673 sec67 4 5 cot61200t673 Math 1350 Precalculus Th e Unwemmr QfHozston 27 sin6 29 sec2 x 31 secx 33 coszx 35 tan26 37 00526 39 1 41 secx 43 1 45 sinx 47 tanx 49 2tanx 51 71 Notes for 5369 The symbol means therefore QED is an abbreviation for the Latin term Quod Erat Demonstrandum Latin for which was to be demonstrated and is frequently written when a proof is complete 53 secx7sinxtanx cosx LeftHand Side RightHand Side secx7sinxtanx cosx 5m x Sin X cosx lisin2x cosx 0052x cosx cosx secx7sinxtanx cosx QED Solutions to Chapter 4 Exercises

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