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26effa06 - MATH 26 FINAL EXAM FORM A FALL 2006 1 Find the...

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Unformatted text preview: MATH 26 FINAL EXAM. FORM A FALL 2006 1. Find the remaining sides of a 30° 7 60° ~ 90° triangle ii' the lcmgerst 5. 11‘ right, triangle ABC has C = 900‘ a = 3‘ and b = \/17‘ find cos A side is 5. a) —3 a) 5. 5J3 ' W7 h) 2. 2% b) «17 8 7 7V3 E) E 2 C) _"17 9 1) 5 {Mg 1 ( -1 _ 2 2 d — ) \/ l7 9 Qfi C) 5‘ 2 e) E ' 9 2. Find sin 0 and tan 6 if the terminal side of 0 lies along the line y = 42: . 2 2 in quadrant III. 6. Simplify sin 30° — 16$i1130° (205300 + cos 30°. N! a 3 a) si110:741:7.tan6=—i ) b) 1 , 5V5 _ 4v 17 l b) Sln6=?:i.ELll6:—— C) 1_5\/§ 2N1? cl) 1 — 4\/§ C) 511102— ,tan9=—4 17 e) —12 4\/ 17 d) sinfl = — 1? .tanfl : 7. How long should an escalator be if it is to make an angle of 30° with ) int? 7 4V1? taut? _ l the floor and carry people. a vertical distance of 22 feet between 9 S _ ‘ ' _ floors? . 40 . . r) 30 Ft 3. If sun? 2 fig and 6 terminates in fourth quadrant, find c059. ‘1 " b) 35 ft _ 8 a) cosGiifi C) 40 ft b} c056 : 2—0 d) 44 ft 8 e) 11\/§ ft c) cost? = i 41 9 8. Find the exact value nf sec 210°. d) C086 : m— 41 9 x/i , . a = — a) — e) ('0‘; 41 2 b fl 4. Simplify use 6 — sin 0cm;2 0. ) _ T 2\/§ a) sinél C) 3 h) mm; d) -2 c) sinfl gfi ('050 e) _ 3 d) c056 HII] 9 6) C056 MATH 26 471' 9. Give the exact value of esc ,—. d :1.) —\/§ b) 2 c) —2 2 d —— l a E) .1 x/E 10. Use the unit circle to find all values of 6 between 0 and 271- for which x/E tan I9 : 7*. 3 5w llfl' H.) _1 — 6 6 b) E? 21 3 3 2r 511' v) _’ _ 3 3 l] d) :1 —:JT 6 b 7r 771’ (r) —, — 6 6 11. If 6° is a. central angle that cuts off an arc of length 3 meters, find the radius of the circle. a.) 16 m b) 15 In C) d) 16.3 m 15.7 m e) 17 m 12. Ila point is moving with uniform circular motion with linear velocity 2 cm/Sec on a Circular path of radius 4 cm, find the angular velocity in. a) 4.5 rad/sec. b) 0.5 rad/Her: c) 4 rad/sec (1) 1.5 rad/sec e} 5 rad/sec FINAL EXAM, FORM A 13. Find all values of (I? for which since = l. a.) —% + 21ms where k: is an integer b) g + 23671", where k is an integer 1r . . c) — + 2km where I: IS an integer fl cl) km where k: is an integer e) g + 2km, where k is an integer M. Identify the Amplitude and Phase shift for the equation 3; = COS ( a.) Amplitude = 1, Phase shift = —7r b) Amplitude = 1, Phase shift = —g c) Amplitude = 1, Phase shift = g (l) Amplitude = 2, Phase shift : 711' e) Amplitude = 1, Phase shift = 7r 1 l5. Evaluate sin—1 (E). a) —% b) g c) g d) “E e) —E 3 16. Evaluate. tan (c0571 E). a) 3 b) g (t) g .1) g 6 e) ? FALL 2006 1 +7: ,1. _ 2 2 ) . MATH 26 tam2 B — 55112 B 17. Simplify 28 1 sec — '1 sin2 B 1 cos2 B H) b) c) SillzB d) _1 c) €032 B 18. Find an identical expression for sin ( a) — sin I 13) cos at c) sin a: d) 7 cos :c 6) tan 1' 33—— FINAL EXAM, FORM A 2 19. If CUfi A : —+ wiLh A in quadrant 11, find cot 2A. m a} b) 4 3 20. If sinA : F with A in quadrant II, and sinB = —g with B in a qumlrarlt III. sin(A + B). a) *7 3 2|. ‘22. 23. 24. 4 Evaluate sin (arcsin E — arctan 2 | no a)5 “3% b)— U1 MC“ ”8 m a: E: i m §’ 2 C}5\/§ Solve sinm+2sinzcosm : 0 ifU 5 cc < 271'. 3’, NH N131 Nil?! ml: tel-1:: Ml? a. . a) E: Nlfi Wifl (I v 01m 6 411' 3 9-. v ml? ml?" 5') V 1111' 6 ) . x/fi Find all solutions for sin 20 = Y if 0° g 9 < 350° :1) 30°, 60°. 210° , 240°, 260° b) 3O°.60°.210°12/10° c) 45°.l35° d) o°,90°,lso°,270° e) 0° . 90°. 180“, 270° , 300° FALL 2006 MATH 26 FINAL EXAM, FORM A FALL 2006 25. in a triangle ABC, B = 120°,C : :30" am} .5 = 7\/§ inches. Find (1 30. Write the equation 1" 2 400519 with rectangular coordinates. a) 10 inches b) 5 inches (2) 3 inches d) 8 inches 0) 7 inches 26, Use the law of (-osines to find a. true statement from the. list below, if C : 120°. a) ('2 = a2 + b2 + Gin/g b) c2 : a2 + b2 c) 02:a2+h2—ab\/E d} c2=a2+b2—ab e) c2=a2+b2+ab 27. For a. triangle ABC" find the triangle-’5 area if a = 4. b : 5 and c = 7. u) 2x55 b) 4 c) rh/E d} 16 9-) v’fi 28. Use DeMoivre’s Theorem to evaluate ((105210 + isin21”}10. fl 2' a)‘?+§ b)_£+fl 2 2 )_\/§_z‘fi C 2 T d) 1—1 \/§ 2' e) —¥i~ ' 2 2 ‘29. Convert (2fi1—2) to polar coordinates. a) (4,330”) b) (6.320”) c) (4.310“) d) (5.345°) e) (5, 335° ) a) 3:2 7 y2 2 4x b) :1:2 + y2 = 3.13 c) x2 — 1,12 = 3m (‘1) :1:2 + y : 4m 2 e) a: +y2=4m FALL 06 MATH 026 FINAL ITEM NO. FORM: :1» kamedeE-LUNH |_I U'l W V m 0 m m w W U U U m w 0 W O b m w m W U m U U 0 W m U U * — graduating this semester. ...
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