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1114W2sf11 - MACl—114 002 003 005 Name Kati Worksheet...

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Unformatted text preview: MACl—114 002 . 003 005 Name: Kati Worksheet 2 ' (circle your section) due October 10, 2011 Read and follow all directions carefully. Include as much relevant work as possible to ensure maximum credit. (5 pts) 1. Convert the following degree measures to radians. a) 450° (reduced fractioninterms offl) ' 6 rr “soo_l : liar!" .___ QSIT = all: 50—3;— [30° 1% ‘l' 3- 3‘ ' - b) 171° (4 decimal places, of; 11; terms of 11:) b) .2 Gigi—I S l")l°‘ .11.. -_ “—7.11. : aficguel 120° 1%0 (5 pts) 2. Convert the following radian measures to degrees. ' (in“ ‘3 (1%0") ‘ ' _ ° a)7—n(exact) 7...: = ”(‘36) -6314 15 15 o a) 8 Li C11 = teo") b) 6.78 (2 decimal places) cons-tsp." = “”50“” = 383 ucs°.-. am (6 pts) 3. a) Evaluate sin 6 . (4 decimal place accuracy). Sin6r=-O.a'7‘il-ll... 3° .ay-oowag \ R ‘-' C [11“] ads .._ a if“, P 1)) Find the exact value of sec —'—6~ [1.11: ii igO’)‘ 93.506 /7 I RE (a e ' b) 3 non so°- WM" =~ “a 3% LE .3. $ 9 c — 6e c. —~ 0. do 53 5’3 3 0R E (6 pts) 4. In a given circle a sector with a central angle of 52.49° has an arc length of 44.65 in. . a) What is the radius of this circle (nearest hundredth of an inch)? a) Li ?' q Li l‘lfl. . P‘s i—u films 9* F: - e A Haas (Mu.es)(lco) _ km“ {A u. u no r : swag?) (senor) b) What is the area of the corresponding sector of this circle (nearest hundredth of a square inch)? i O (a, 8. i I) . L b) : In a I_ a as‘ Erie ‘*' 30‘8””) (“NYE-go": memes... 3. 2 (4 pts) 5. TWO pulleys are connected by a belt. The larger pulley has a radius of 10 inches and the smaller has a radius of 6 inches. In the same time period that it takes the smaller pulley to rotate through an angle of 60° , through how many degrees would the larger pulley rotate? @ ce.=s= we... Ans 3G6 - __ . a (l0m3(9.20 - (G Ih) (60) a. m PM“? limi- . = m | o :7 g _ 15 L3 kisser ('9: 7 6:6?!)h .1 IOI‘n (00 IO (Goo) .. 136° "fi'de‘fi' to 5'0”" . . a (16 pts) 6. a) Given the unit circle below, locate and label the location of points A and B, given that the counter-clockwise arc lengths from point (1, 0) to each point is as given in the table. State the exact coordinates for point for A, use two decimal place accuracy for point B. (X) ‘10- — (C05 5 $ MS) I 5—} Are lengths C d' t ‘L '- oor ma es 3. 1)) Suppose that at arc length 5, the unit circle has a point with coordinates (ELIE) . Which of the following points must be on the graph of a sme wave? Circle the letter of the correct answer. lbw} am when“ SJ 4L; 3“ 1M. Vxlw. ks h . a) (111,11) 1)) (8,111) (1) (111,5) 8) (11,5) f) not enough information 71'. c) Find 3 (exact value in terms of 1: ), given cos 3 2 ———2—- and it < S < -— . Label this point on the circle as point C. c056: J; M11 Iso°<e< 370° $ 9: 2m" -. we"; 'irr = ...._ . ' wr Cause") we» 6 “WW-awe (6 pts) 7. The formula H = 3.3 + 2.9 sin (0.5(t _ 1)) represents the height of the tides, measured in feet, at a beach where t represents the number of hours afier midnight. Use this formula to determine the highest and lowest height of the tide at this beach, as well as the height of the tide at 2am. Express all answers with one—decimal—place accuracy. k‘lqlflG-Si '-' UQV‘. Sidin' + GNPHM 3 3_3{_a.q =G‘D. .6, looms-l"L oer. Ski-‘4' '- QNPllM =3.3-a.<u OH high t . C 3+ 3-4 ' @ 9.0M J 4:; lowest: O.Ll H. H: ass-tan Slit (6.604)) : m ' 2am: Li 9 fl" y: (1+ «sin. [to (x 49.)] [041 Mpiivi-wfie, C‘- cert-1 call 9% - ‘ W ‘ At~ k ma 1‘ Mo -‘r m In IS uw’ncail n-flo "—' '-‘- mi ’ P M“ 9 3 ‘5 P Y Ukmy‘ b Pe Ckwizowiafi) (8 pts) 8. Graph each function over [0, 211:]. Your graph should clearly contain the correct high, low, and median points. Ampii'i‘mlt ‘-'- 6 ampliiwie = ‘1 ‘1 z} ' MBA. Eli-:11“ 2'= = [-5] n‘odlnrfl ‘- a)y 6sm(2x) P t = P. (‘1 E’) b)? 4cos x 2 [game ski“: fag) _ canine. Loam. 1923i»: ken: 7 ism ’TLcLs is also +14. graph a? y=Ltsuiax. LMPMsath-lCMYowexiatamwng? (8 pts) 9. Graph each function over [0, 27C] . Your graph should clearly contain the correct high, low, and median points. th‘ficd skfi: '2_ cup Y=-1+6com ucrl-tgdi. sic.“ = Maw.» a) y=2+4sinx ObWLpliix-ude, r, L} b) yzécosx—Z mmptl‘i-Me: 6? warm (—2» a 5; WW = aw (n :13 vxo veritcaQ shit“ MP\3+M&£ : H ‘ - an; PQU’LOfl, " 3 (%: Es:- -tl- l a F! v 9km, 5&3.th 3x—n’zo °n<=rr vac?) 2;)“: Hcos[3(X-§)] is Maud/t" Fovm Por- WA; rplwciim - 4 (12 pts) I1. Find a formula so that the graph of y = c + asin [b (x - (1)] would look like the following. The graph has a high point a low point as shown Label the beginning, middle, and end point of one wavelength with appropriate coordinates. ‘ _ ” y: sgwag 1M" iris-(W503 I y _ “in-5"? '- . . (DUETHQOQ shut“: w—¥=1§T=38 “1 @mPli-lwiz CO— 38= '19. 331$ 6.. (ea) 33-46 -'-'- 33 230-110 = ROAM? pathofi LLC’ : 60: quark!- poan -_ 1r;- ‘ aqo—so-raqo —— pen'aoQ - _ mo so no no ago me ~ . _ . _______________________________ 4. 11-”? __________ it _____________Eff-iii:-.‘.‘f_’-__f_° ff (8 pts) 12. Draw an accurate graph for each of the following over the interval [0, 21:] . Your graph should clearly pass through key points and exhibit asymptotic behavior where appr0p1‘iate. a) y=1—3secx b) y=4cscx , z - : , (8 pts) 13. Draw an accurate graph for each of the following over the interval {0,12%} . Your graph should clearly pass through key points and exhibit asymptotic behavior where appropriate. b) y = 2+2tanx ...
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