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Unformatted text preview: Math 113 EXAM II, March 11, 2003, (1 hour). NAME: Instructor: TO RECEIVE CREDIT FOR AN ANSWER, YOU MUST
SHOW WORK JUSTIFYING THAT ANSWER.
I. Give the EXACT values of cos 5’41, sin 5%, and tan ii. (10 points)
II. (20 points) 1) Find a number c, with 0 S c g 1, such that sin‘1 c = cos"1 c. 1 2) Does there exist a number 0 < 0 such that sin“ c = cos_1 c ? No credit will be given for an answer without justiﬁcation. III. Using the graph of the sine function below, ShOW CLEARLY m0 = sin—1(sin $1) + 27r,
on the :1:~a.xis. (15 points) IV. Evaluate EXACTLY: ' (30 points) V. Verify the identity: (25 points) sin(2;c)tanx = 1 — COS(2.’12) . VI. Draw a CLEAR ﬁgure corresponding to the following ‘word problem’. Do not solve
(no question is asked!). (20 points) A plane is ﬂying over Madison. Straight ahead, Picnic Point is seen at an angle of
depression of 40°. Governor Nelson State Park, also straight ahead, is seen at an angle of depression of 10°. The distance between Picnic Point and Governor Nelson State Park is
3.8 miles. VII. (20 points)
1) In the ﬁgure below, AB = AC. Show that ADCB : w. 2) Evaluate the following ratios in terms of the values of the trigonometric functions for
the angles :1: or 233. E
D E
o 5
E E
9 6E5
912
 3) Given [AC] 2 L (so, also AB = L). Using the above ratios, give the values of: IADI ICDI ll DB 4) Write DB = AB — AD. Which trigonometric identity does it yield? Math 113 EXAM 11, March 11, 2003, (1 hour).
NAME:
SECTION: I} Instructorﬁ TO RECEIVE CREDIT FOR AN ANSWER, YOU MUST
SHOW WORK JUSTIFYING THAT ANSWER.
I Give the EXACT values of cos —, sin— 5" and tan5 7‘ (10 points)
Cw SIT_ __ ._l..
vb T Vi
— I
w) Yr : " ——
“‘T E
M5 ”‘53:? \
(MK—LT  Cavilr .
(20 points)
1) Find a number c with O < c < 1 such that sm 1 c — cos 1 c
~ I
_L C. : ——
f V3.
. 11' IT
DM‘C— LL: (‘Dccwg bwlgziFlWt ‘1‘)1‘ /q< /)
(mfg 1 {f (Etc—aw): Cm‘I:iV.Lana as T—E Q 1T» 2) Does there exist a number c < 0 such that 5111‘1 c = cos‘1 c ? No credit will be
given for an answer without justiﬁcation. N0 aﬂwoup “'/q_ {Mic s “71 ’ A c<o w: We» _._._
_’_—. ,W, MAM ~n72gmi’c<0 .9115“wa ongD_‘C <TI‘. III. Using the graph of the sine function below, show CLEARLY :50 : sin'1(sin $1) .— 27r,
on the (bands. (15 pomts) IV. Evaluate EXACTLY: (30 points) cos (% +tan”1(~2)) .
$6}! ezim‘WZB . so MAS—“2 m1 “£49“ Wt \ %’\\ﬁ’3% C8016:
609119 $MLL¢ C00 9 )0 Chem: "n/z(9 4 {CW/LN \+\‘0ML9: ‘ 1? \5_ _l+21f3‘
=7Tr‘g‘7fﬁ H‘s V. Verify the identity: (25 points) sin(29) tang = 1 — (303(26) . budge) lMQ: Zbﬁecma Awe C039 2 Au‘AZG ll _ \ @329 VI. Draw .3 CLEAR ﬁgure corresponding to the following ‘Word problem’. Do not solve
(no question is asked!). (20 points) A plane is ﬂying over Madison Straight ahead, Picnic Point is seen at an angle of
depression of 40". Governor Nelson State Park, also straight ahead, is seen at an angle of depression of 10°. The distance between Picnic Point and Governor Nelson State Park is
3.8 miles. _ __‘;;(_ n__ L40” VII. 1) In the ﬁgure below7 fAB = [AC]. Show that ADCB = 0.
Z. BC A : V Sch LEBA: v . so at»
1% vavaQA AFDC 26+'V+v: "luthMWV‘Wbﬂ 3CD LDCB: \80°
%¢_V I A0 V
:9 (20 points) 9o°~ 6  2) Evaluate the following ratios in terms of the values of the trigonometric functions for the angles 6 or 20. '23:: @929
.igfzbw2e
JI%IL= tame 3) Given IACl = L (so, also IABI = L). Using the above ratios, give the values of: mm: L. 0:229
L buLZQ ICDI H L ALA/:29 )Com 9 lDBl 4) Write IDB : IAB! — lADi. Which trigonometric identity does it yield? Lmzamaz L — 1—0229 $0 gamma love L3 Mime: LCD?» 19
(6w; \‘dlmk'lv I‘VWWJ \M E\ . B
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 Spring '07
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 Trigonometry

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