113-rosay-06fa02-v2-key

# 113-rosay-06fa02-v2-key - Math 113 p EXAM II NOV 3 2006(1...

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Unformatted text preview: Math 113 p EXAM II, NOV 3. , 2006, (1 hour and 15 minutes). TO RECEIVE CREDIT FOR AN ANSWER, YOU MUST SHOW WORK JUSTIFYING THAT ANSWER. I. (NO CALCULATOR) ' (15 points) Evaluate [BEI (the length of the line segment BE) in terms of a (the length of BC) and 0. Justify all steps (as usual). p . ADEC+LDBA= ao° (bewa4A%C=40\ e + L : 40° (Vx‘wuVV/u‘wuoﬁl so [_ DEC; 9 II. Using your calculator, ﬁnd an approximate value in degrees of an angle 0 such that: sin6 = -—% and 90° 5 6 5 270°. Explain. (10 points) WNW MVP—9;”) w 0M be“ (mmgﬁcaég . (DWvCﬁ IBWCMOH ><\-:-I>Cv\>< ) wc Law. a N Q. \525270 «mum: Mmzzmﬂ .. -— E.- C‘O 6” , Jbt‘vvl So 9 = ML?) (ooh Aeox‘VcAvwove MOE-1 \$1 LAM/Iqauo MAWIKOMN qﬁw We» to ba‘owlk. 1. III. Evaluate h. L M (’8 Comma“ (25 points) 5% 51m”- 2 (gm and qﬂrua = . I _,___. "Io A w, QC Immsmchax mass.-. d‘hﬁ d:m“§3:«; ’)_\.8° . 7D “£2 Tva Judion wao M0‘r meek} . \MJeek bCVHi :\}Ivcoo°‘ok (lawn-Avid70\ 95 Doug: \Jl—"ﬁgy' OW?» AOQANVCG“: a. ( wlu'\‘c : £31 Cl __ )C‘)?" : 5 5 ex 3 k9. + XL 3 37' 1 . \$udva‘lmpV he MX, dxw eke/V ' AW; IV. "Evaluate the angles oz and ﬁ. (25 points) A Law 9% mama»: ., 1, L 2— D /61/;E\C CL: mwuzmnmmw \\ («@103 98.1.9- V. Show how to derive the double angle formulas ' (14 points) 2 cos 2x = cos ac—sin2 a: = 2cos2x-l = l—2sin2x, from the addition formula cos(:c + y) 2 cos x cos y — sin as sin y. Take, \/—_-. x I Ck“ allde bumdle («Wk ’01: “spun: a992x: CmXCmX—BVC‘X MIX : Qm1x_szZ"¥ 2 '2 1 [Wm may: Cobq‘x-}bu:1)(’ (\—hw%\_bw>1—\—i/Am¥ Cm N: am- Bwlx — catnip (wmﬂM— (Mo/ale VI. Is the following a true identity: cos 33: = 1 —- 3sin3 x ? If it is true, prove it. If it is not, show it (try to ﬁnd an obvious reason). (6 points) wile» x: 1;: Lama: l—B: _7. EM Cw (Raw : o - T’QAQ\\AQAA\/\‘\/*A (o wrwvér. VII. Give the exact values of d. NO CALCULATOR. (20 points) You can use the formula tang: : g/\ A Dome“; WA VQVCQOBV‘)‘ A 44 WP/Wu/M T‘QN Qva-Mﬁ'mcow TeAune/w 010% moving”: 2L. 9° heck: I} A w m :fL(=iY;Pj Q. s V m - MW s “a .. x h m; 17 ﬂ ‘5‘ I 5 . __ 9, In (Le lbw/mam)“ MIG/(NV wwxcx, (ﬁﬁAB : \rovw)( .. 1):; VIII. Draw the axes, in ordte to get the graph of ' (15 points) \l? y : 2cos(3x+-72:)—1. Put well chosen values of x and g on the axes. In particular these values should make clear What is the period. J) '\<\] A‘Mb‘ﬂwm occwg J [A 4‘? g, 3, 6 . ME: A ab 9 :0 ml: u < 2? H I w No cALCwLAToRg IX. Show on the ﬁgure the angle oz (in standard position) such that: 217 S a g 37r and cosa = —§. Give the exact values of: sin a, cos(a + lg), sin(a — g), and sin ' (30 points) Nob: va mo\' wow?“ \‘01 bﬁnw 03% din Vume 9°90“ [build-x Quid :\ W‘JM’J .g_ q DW&:15' \$vrnm mi 01 >,o (q—«AJAM‘FE\ A a__1 ‘7 )bwoL:+\T-Z:5:—. ‘5'- ANSWERS: sinoz: l cos(a+£)5= Coed TF buloleLTT —- -" ‘5 3 ‘ -— "4r‘3 6 m 4‘ 4"?Z~?1‘ [0 ~ ._ ' TF..3I 4N3 __> 4434—3 NwMﬂﬂ[email protected] ,_-~__,_ ,_, 2»: 2L 1 _. 3 7/ V73 ...
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