Solutions to Exam II Ma120(Purple version), Su05

Trigonometry

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Unformatted text preview: Math 120 Trigonometry Name: ; 01.017 DH) (32 Summer 2005 RWJ Part I: Memory Work (1V0 notes, closed book, no calculator) — 6 minutes 1. (16 pts.) Fill-in the table with exact values: 2. (12 pts.) Fill-in the table: Function c» .3 cm w (“90/ 9") Math 120 Trigonometry Name: 2L3! 10F; (.32 Summer 2005 RWJ Part II: Calculator Work (a calculator and one page of notes is allowed) — 15 minutes Note: F our-digit accuracy suffices an approximate calculations 3. (12 pts.) Determine the following: a. sin200° ’-‘.-' 1342;; b. sin200 '33 —-,9733 c. sec"3 = (0.5“ (3") d. tan"(2) g ("D—H 1: 1.7.310 4. (16 pts.) This problem concerns the expression 4cos x —105inx.' a. Rewrite this expression as a constant multiple of a sine function. That is, rewrite the expression as A sin(x + B) for some A and B (tell me what A and B are). Show your work. ~ ‘2. 1'+- ~10) 5 “4 L4) [ . ('3'— (onc + "JE- 5117:.) 4msx—(ojmnz JUé J32 J77;- ¢ J77; (53w costs 4” {0}», 5M K) 3 {DZ (sikéfiyg) VWELAeA. ”5 5lacxi’1'751l 1' WI b. What is the maximal value of the expression? .497 We ’4‘" “’5"? W7? ’51», c. Give me one value x which maximizes this expression. ./ Div?” 70? 1.76“ = (IT/1.. 7 ._ ,, (:12) [\j' (0’ . W‘ [’7 1‘“ 704.;“31—33) 7“]:‘5 Iv 3 0 $ 2.76“ Math 120 Trigonometry Name: 2mm”; (52 Summer 2005 RWJ Part III: Work by hand (no calculator, one page of notes only) — each of the remaining problems is worth 9 points. 5. Give an exact numeric answer for cos(2 sin”l (3/7)).Show your work. 0‘4 05 {29): («15113-3 4-: 3141 . ‘0’ (157“???) = 1—- 1C 5.; wrflfi’fifll ’v‘ I- '2. (3/7)?" «a , = New 22'. ‘H °¢ 4" M/wvn 6. Give an exact numeric answer for tan[tan"(2/ 3) + tan" (6)] . Show your work ’(T’KCol+f)= h«a§+«(1ne l—zbmot in“? 5+; 4.1-» [44»? 5%) 4413(4)] 5" 3 = no 0k (9 P‘éflg) 7 7. Write cos(3x) in terms of cos(x) and powers of cos(x) m. Show your work. @ (95(2K’r7c) "' (0517‘ (9)7: — 51:11-62 513x H =<1coj‘7c ~I)(of 7C —-' C 15';7<C:>J"<)5': X = lcasak—(wx —- 2.559% 655% : '2. 6’33“, —cwu< —- 2C(-Cos"1c) (~52: " ¢40537c - 3(w7c 8. Exactly evaluate cos(tan'l (3/7)). Show your work. W "7 A7 W 37/1. +fl/1 51>“ ’{1‘3’3/7 [#7 W)J’b¢ (Ch 7wévud CL) WJT’W 3175—. A Vim/7 3 we. unit (0.! I7 V6097 =7 V‘ (Ijrj': iii—Cd w 50mm} (B) 9. True/False (circle the correct response in each case). Look at the list of formulas discussed in class to answer the following questions. No reasoning necessary. @or False: If we know both the value of tana and tan ,6 then we can absolutely rmine the value of tan(a + ,6). b. True orafijs If we know both the value of cosa and cos ,3 then we can absolutely determine the value of cos(a + ,6). c’r False: If we know the value of tang then we can absolutely determine the v u- of c0320. J d'r False: If we know the value of cost? then we can absolutely determine the va ue of cos 26. @ [email protected]‘*P)‘ mxk’f‘w ' 141%me 5,9 ‘er 41nd; hale 4m Ismsk «(TM—\[oé'r/B) anaermy If? (0500-?) = 1&5 .4 cup —— sure: slut]? in? («95 94/ (as? awe moi" WAJD 4;ch {’6 (04+ F) ((4145? Afir‘él/‘MILQ 51:4, Sigfl (pmplldvlv 9w“ 57" °(/ a’f) s—f C9 bale-e "”19 Spi‘fl'vwkwh‘? W" 1+4»- 19’ 6&5er (9.32.6 @ évéwe heft?“ gpmywma KW 6'55 >4"J a“ aches. 6’519 10. True/False (circle the correct response in each case). No reasoning necessary. a. True or.or all x we have sin'1 (sin x) = x. b @. r False: For all x with —1 .<_ x $1 we have sin(sin'l x) = x. c. @or False: For all x with 0 s x S 7r we have cos"(cosx) = x. d. True 9f 3. the graph of a function has the property that any vertical line cuts the graph 1 . most one point, then that function has an inverse. A. 6%" (flk'fl’) =t 11', law lfi5hm¢ W a”- St'u“ (D) ...
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