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26e2fa06 - MATH 26 EXAM II FORM A FALL 2006 1 Find all...

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Unformatted text preview: MATH 26 EXAM II, FORM A FALL 2006 1. Find all values of :1: for which csc(a:) is undefined. 4. The graph below is one complete cycle of the graph of an equation containing a trigonometric function. Find an equation to match the kw graph. 2 1r b) A + AW: 2 7: c —— + 2hr ) 2 (l) — + 2km" e) kvr 2. Find the period of the function y = (115 (E). a) 571' b) 107: C) 27r l d) — e) 5 a) y=—3+3Hinnx :5. Identify the amplitude and phase shift. for the equation 3; = 2 sin (29: + g). b) U = 4 'l‘ 5 5‘“ 7795' c) y = 5$lIl1T£E 71' a) Amplitude : 2 and Phase shift : —Z d) y = 2 k 48in mm b) Amplitude = 1 and Phase shift = —-E e) y 2 *4 — 55mm): c) Amplitudc = 4 and Phase shift = E ' 2 , «E _ ‘ . _1 1r 0. hvalnate 5111 75— . d) Amplitude = 2 and Phase shift : l 2].) 7r e) Amplitude : 1 and Phase. shift 2 E 3 71- b _ ) 2 11" c) 6 1T d _ _ ) 6 7r 9 _ ) 3 i 6. Evaluate cot (tan—1 Z). a.) i b) 74 (1) 4 d) x/E e) 41 MATH 26 7. Find the indentical expression for (secs? + cot 103111.13. EXAM II, FORM A FALL 2006 12. Il' tan/1 = VB, find tan 2A. a) tan :1: ) V 13 a __ 6 b) sccw x/fi r) tan 1' —i— c053: b) T d) cos :r 0) 2m e) cot .‘L' + sin 3' m d) 7—— 4 . ' a: 1 - ' 8. Simplify L w. e) ‘2 13 1 + cos :1: sm 1‘ . 2 _ 4 3 a) 2586 a: 13. If sinA = F with A in the second quadrant, and sinB : 7 with B O t. b) 20.059: in the first quadrant, find ces(A + B). c) 2sec1v \/§ (‘1) 2:25:31: 6.) ? e) Ecscgm 24 . b __ ) 25 _ _ fl 9. Find the identical expression for COS (.7: — C) 7? l a) — sin :1; d1 '- E 1)) sin .1“. 1 e) ‘F O C) Ian .I‘ d) 7 cosrr 14. Use half-angle formulas to find the exact value for (‘05 105° 0) cow: 1 + x/i u) 2 10. Write the expression cos 7.]: cos 3.7: — sin 7.1: sin 33? as a single trigono— metric iunr‘tion. b) _ 2 7 J} 2 . . . 1 d) (0131051? 9) 5 b) {'05131' I (i) 7 7 C) (305141: 2 Ci) COS 123' ) 2 + “3 e _ e) cos 1 11' 2 1].. 11511111 : L V5 with A in quadrant 11, find cos 2A. 15. Evlauatc tan(sin’1 85c). x/64m2 7—] a) 81! b) V 1 7 64:1:E 8:); c) 8 xv 1 7 643:2 d) 8:1: V’ 1 7 64$2 9) 8:]? 6/13: — 1 BJJYITJ 26 16. Rewrite the expression sin 15:1“. + sincr as a product, a.) b) c) d) e) 17. Solve the. equation SCOSL+1: 3cost for t if 0 :1 t < 21¢. 19. Solve the equation cscB + 2cot9 = 0 for 9 if 0° 5 9 < 360°. 2 sin 71' cog Tm ‘2 sin 6:1: cos 7:1: 2 511183" ms 71‘ 2 cos; 63w sin 73: 2 sin 7;? sin 73: 1T Fm" 2’? 7r 57.‘ 6'? 2w 4w Y‘F 7n 1171' F“? .‘317 51w 7’? 7t 37: 7r SW 2‘ 2 ‘6‘ 6 1'? 511' Una—.— 3 '3 O‘W‘Eg’fl 3 3 0%,:‘5—71- 6 6 17 311' 7r 5w 2‘ 2 ‘3’ 3 30“,330° 30°‘150° «150.135O 12022400 225°, 315° 3 IE){£XDA II,IVC)I{BJ It FAIJJQUOG 2U. Solve the equation 2c052m + sinm — 1 = 0 for x if 0 S n: < 271-. a) b) c) d) 7? 11' 511' E’E‘ 6 1T '71" 311' E‘F‘? 7r 771' 1171' E’F‘T 71' 5% E’”‘? 277 417 "?’"§ FALL 06 MATH 026 EXAM 2 ITEM NO. FORM: A l E 2 B 3 A 4 D 5 A 6 C 7 C 8 D 9 B 10 A 11 E 12 A 13 B 14 B 15 D 16 C 17 C 18 A 19 D 20 C ...
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