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# Review Sheet for MATH 111 at UA

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COURSE
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PAGES
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KARMA
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This 3 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Arizona taught by a professor in Fall. Since its upload, it has received 18 views.

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Date Created: 02/06/15
Math 111 answers to review problems Multiple choice 1d 380 2a 390 3a 40e4 4e246 degrees 41a 5b 420 6c 43e23 right 7d 44d 8e 45d 9a 46c 10d 47e2pi3 11b 48a 12a 49d 130 500 14a 51a 15b 52d 16a 53d 17a 54c 18b 55b 19b 56b 200 21a 22a 23c 24b 25e491ft 26c 27etm 28b 290 300 31a 32a 33c 34e4 J5 35c 36c 37c Partial credit 2 X 728 cm y 4767 cm 3 X 645 cm 6 5719 4 X 831 cm a 2792 5 3 5 5s1nX 70SCX itanX 7 3 5 2 6 a On the unit circle centered at the origin start at the point 10 and travel along the circle X units clockwise ifX is positive Stop at the point ab By de nition sin X b After traveling one complete cycle around the circle the values Of b will repeat in the same order so sin X is periodic b On the unit circle etc tan X ba As a approaches 0 ba increases or decreases without bound The value ofa is 0 at X if and 2k plus these values k any integer Theses give us the X values of the vertical asymptotes c On the unit circle etc cos X a As long as we stay on the unit circle the horizontal coordinate a will stay between 1 and 1 inclusive 7 cos 2X cosXX cos Xcos X 7 sin Xsin X cos2 x sin2 x 5 1 2x5 10 X 149 372 670 901 appr0Ximately 11 X 589 982 2553 4124 appr0Ximately 12 X 96 511 app 13 a 12 b 732 14 a32 b 12 15 a b 4A5 16 a y 2 4 COSIZ394X6 others possible b y 200 100 sin5 IZ39X others possible 17a 7r6 b 5 c 1 d1 x2 e x 89 l x2 18a y 4 2 cos Ir2X others possible b y tan 5X others possible 0 y 7 3 cos IrX others possible 19a 24 b 6 14 22 others possible 0 4 8 12 others possible d y 21 3 sin Ir4X4 others possible 20 all angles are in degrees a A 4442 B 5712 C 746 b A 744 B 1406 C 15857 c A 3937 B 6263 c 771 ft d A 4478 C 11022 c 1332 m and A 13522 C 1978 c 4 m e A 255 C 11645 c 937 cm fC90a386ftb46ft 21b 0 X 2 app QII X 43 app QIII 22 b c X 39 QIII X 55 QIV 23a 16 8 4 others possible b 16 Two average values are at least 12 a period apart These two are 8 units apart so the largest possible period is 28 16

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