Solutions to Exam II Ma120(White Version), Su05

Trigonometry

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Unformatted text preview: Math 120 Trigonometry Name: jam)“ 00“} Summer 2005 RWJ Part 1: Memory Work (No 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 ’ w w ("I '3 Math 120 Trigonometry 50 Lorna”; Summer 2005 RWJ Name: Part II: Calculator Work (a calculator and one page of notes is allowed) —— 15 minutes Note: Four-digit accuracy sufﬁces on approximate calculations 3. (12 pts.) Determine the following: a. sin100° ’5 ‘931-3/ b. sinlOO ’2‘ ﬂies?- c. sec—‘5 :: (05"C d. tan"(8) 2“ [KI-+£9- “a‘ (.3m4- 4. (16 pts.) This problem concerns the expression 2 cos x — 8 sin x. 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. @2qu- = 68 513n7< «a» 7 —: "5? (sin/7mg + (059 ﬁx“) . ‘2.~ #8 ié’jﬁ’XSIKK. : @(E‘g‘oﬂ-ﬁlk W2? 94407”) I“ 31”“? b. What is the maximal value of the expression? -~-* g. (a; 7 ' iv} 0. Give me one value x which maximizes this expression. {D “J x+ 2. Wee = “TV/2. "‘ M fawn 9.35 (A) Math 120 Trigonometry Name: 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(2sin'1 (1/3)). Show your work. 0% (05628) = I» 25'709 J» M M037) =’ I» 2 [arch-mcgpf MC 15” W W 9 I h 9 1.. ~ /»z(é) —~ 2 1 7 6. Give an exact numeric answer for tan[tan" (1/ 2) + tan"(1/ 3)]. Show your work. iauéwﬁ>= fﬁiii—fiﬂi 7. Write cos(3x) in terms of cos(x) and powers of cos(x) o_nlz. Show your work. Wz‘c‘x‘k): cmdm— add?“ 8. Exactly evaluate sin(tan~1 (2/ 3)). Show your work. ’9 vhf/hum “me/“7... wwa7=2¢3 W}* k (L. [’7 r 'h va‘l 21* 3‘ =J15 L‘rs' ’7 ’3 5? 9‘ u)!— wav" ”’7 Two " _. V‘)7k9 Z; 9!» .- .. ’7 r m ﬁow’W CR) 9. True/False (circle the correct response in each case). No reasoning necessary. a®r False: For all x with —1 S x \$1 we have sin(sin'l x) = x. b. True 0 For all x we have sin‘1(sin x) = x. @r False: For all x with 0 s x S 7: we have cos'l (cos x) = x. d.< grue)or False: If a the graph of a function has the property that any horizontal line on e graph in at most one point, then that function has an inverse. b 511‘" {Jim 7?] {IT , J36»— MJJaW‘L . W ﬁlm" (45) = O 10. 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. a. True of we know both the value of cosa and cos ,6 then we can absolutely determine the value of cos(a + ,6). S. TrueSor False: If we know both the value of tana and tan ,8 then we can absolutely me the value of tan(a + ﬂ). r False: If we know the value of cost? then we can absolutely determine the r - 6 cos 20. dqﬁayr False: If we know the value of tang then we can absolutely determine the va ue of cos 26?. ll? Cp}(°<+f3> 1‘ 00504605? —- .5in .511? SIWZ¢ ax V 51;.“ «VI/Cf (v.5 0‘, 66.5% ...
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