02faex2 - Math 113 EXAM II Oct 28 2002,‘(1 hour NAME...

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Unformatted text preview: Math 113, EXAM II, Oct. 28, 2002,‘ (1 hour). NAME: SECTION: Instructor: To receive credit for an answer, you MUST show work: justzfying that answer. FULL CREDIT WILL BE GIVEN ONLY FOR CLEAR AND ACCURATE FIGURES. I. Given sin9 : % and cos9 < 0, keeping exact values evaluate: (20 points) ‘ ‘ bazemta =\ we sin(7r— 9): AW 6: “5: a. 20 sin(7r+9):-—131Me = " é“- CO/be: 2.5“ \ (9 < o sin('12£‘—9)= C01) 9: 2F gUN'c’ W V? .9 Z 9 2 sum-721%): ewe: 2.3077 Cover— 3? r “ b Based on the information given above, is it necessarily true or possibly true or impossible that 9: Sin—1%)? II. The graph shown below is the graph of the function y : cos(3m). (30 points) What is the abscissa of the point P? If m1: —-5—-g' ,give the exact values of $2 m3 3:4 3:5 and :36. Give the exact value of Cos—1(cos 3x1). X = “WAD—dew. xivx ,X=-><., x5=—><5 1 bLCOMI’Q. Q9/700<\1E$Tr‘ III. Given sina = % and tan a < 0, Evaluate cos(a + lg). Keep exact values. (25 points) ~ 3. \ 9' 2 .8. C60 2 M -\_ b w d z I HA QJUW Caro 0t a) $CV\Ce \roMeHo awx minim, C0201<0. _ -\i_3__. ___... $0 Cosd- 3—. .5 6 5 . -101 .03__‘__‘_ : -2W—J “ 3 z 5?— 6 IV. Disprove (by a counterexample or a short and clear argument) the identity (20 points) cosw + sin 2:1:_ 1+sin4m :3cosm. Fowxzo WHMWJW 2‘ but 3mx=3- \4—Au29K HO By using standard identities, verify the identity sin 20 = (1 + cos 29) tan 0. (l+m29>\‘ow\ e z Q+ amiam {we m9 100016 ’BWQ :ZbV‘AQC‘aQ ' we 2 Male ‘4 .— V. Draw a figure corresponding to the twofollowing ‘word problems’. Do not solve (No question is asked!). (20 points) V.1. Two islands A and B are 9 miles apart. Island B is south—east of Island A. From a boat 0' one sees island A at an angle of 10° east of north, and one sees island B at an angle of 35° east of north .......... V.2. To measure the height of a tree a person walked a short distance from the tree and found an angle of elevation of 44", then walked 25 feet farther and found a change of 14° in the angle of elevation ..... VI. In the figure below: » (25 points) 1) Evaluate the angles a, [3 and 7 in terms of 6. Give brief justifications. 0(2 9. (QM/KOO AD MA CF AVE, pavafld\ d\+(5:: 133—8 (Y\‘bl«VVfl\‘a/~Ata£k ABC.» ’AD [5 :- Jig—29 {2 $45 ("'WMMWQ‘ CFBM 00 ‘3”: 29 2) If the line segment AB has length 1 (so, also |AD| = 1). Evaluate the lengths of the line segments CD, FH, BC, BF. Leave your answer in terms of the trigonometric ratios of the angle 9 and 20. |CD|= lP‘Dl \“omG: lwe (Mb/RV l/VQOMUQA ADC) IFH|= [Cbl : \“aM 9 IBC|= lABltmgleQ (“WE‘VWO‘M‘KQ’LABCB IBF|= [Eclmx‘z ’WQ 59326 (“gamma BFCB 3) Compute the'length of the line segment BH twice, once using the above results and more directly, in order to get a geometric proof of the identity of Problem IV. 0 chfi lb Oxbow 4943;»ng ;Q‘l c0926) ‘Fowx 69 13 “0% U?» MW ””693 A “B L c [em—- Mm: 19: MM Sew QAAHPNECJ QWK M: 2 o 1 Q+lee) we [aaiop’xoolia vaflkok {)ot. OSefiq)&AC—l&£~ll¥\l V) A 4 H D Veep/3A Q90, 4w (9%) ...
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