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Unformatted text preview: MAC1114 002 003 005 Name: K E El Worksheet IA (circle your section number) due Sept. 7, 2011 Read and follow all directions carefully. Include as much relevant work as possible to ensure maximum credit. (8 pts) 1. Let 9 = 60°. 0 6 O ‘ 0
a) State a positive angle that is cetenninal with 9 . (90 + 3&1) "5 L‘ a0 a) Li, a0
a o a °
b) State a negative angle that is coterminal with 9 . (00  3 60 = " ‘3 00 b) m g 00
a
c) State an angle that is complementary to 0 . q 0 o _,,_ (no 0 r. 3 O O c) 3 0 (1) State an angle that is supplementary to 9 . (4 pts) 2. If a twirling ice skater spins at a rate of 54,‘ 000° per minute, how many rotations does she make in 4 seconds? SHOOOb r m , j Mia'i'low _ ‘ Ans:_L_()_
1 \meie (00 38cm 7360 c, « Q  5 mk’ttmt per 58%;). a, LICQE)‘: t0 roiwiims {M Ll Semitic (7 pts) 3. a) Find the smaller (positive) angle between the hands of a clock at 6:50pm. Assume the hour hand has moved
appropriately (the hour hand moves in proportion to the number of minutes compared to one hour). Sack IIWM : 31939:? 300 50.3: M 6:60 a» km kw has Wt ‘55:“ a?
“a. bony ‘OQW (0 MD. '7 J {QM/has maxim.
¥=SO 59W ‘RAL 7Q~Mcbck MW
it“; how W is eafattws. 3000+? east 1)) Through honr many degrees does the minute hand of a clock rotate in 2.3 hours‘z‘; "Tim, Mir/twin. [AM Cmpieies aw. mlwhm Per Imam. b) (3330
9.3(1 metalw) : as (3090‘): 838'” (4 pts) 4. Compute 62°53’15”—34°58’22”. Express the (exact) answerindegrees, minutes, and seconds.
(03°63'15” et" na'ss" Altman‘s't'ss"
.s 6932'? s”  3u° 68
4, 61°16'15“ "aver1' 63>" (6 pts) 5. a) Convert the angle 86°15'28" into decimal degrees, with four decimal place accuracy. 86° .12.” 2.5:. ° . aims:
{Go 469606)  seesaw... b) Convert the angle 4.2561° into degrees, minutes and seconds, accurate to the nearest second. I
H°+.osct(coo') = wism’ mm:
We’vsoocouu: new" (8 pts) 6. a) Find values for angles A and B. Assume the diagram represents two parallel lines intersected by a transversal. the = \eo" aw
A:(5x+5)° 610,5 4. 3xua5 2. \80 B 60 o
%x  :20: no "—W
W “900 Ft: SCae‘Qtv 130
X’ 35 'B= Mao—29 50"
b) Solve for x given that the triangle shown is an isosceles triangle. b) a! 6
132° _ Qx+l3Q=\%O
6 ax=h8
‘° X x=au (4 pts) 7. At a certain time of day, Joe, who is 5 feet 9 inches tall, casts a shadow on the ground that is exactly 1 foot 11
inches long. Lisa is exactly 5 feet 3inches tall. At the same time of day, how long is her shadow (exact answer in feet and
inches)? 10% Lisa” A (Hi cit?»
mm. 69‘“. 7 I “5...: 3%. —_ ‘—
63 as 3
33in x (Cross mmiiitaiy)
. W $11.33» 35¢ ‘3 633
‘59sﬁin \€+"li“' K‘Qi En. : ifi‘ Qt}. 3—09. is 3x Fuller MAM. his swﬂmis [ea/sila List» is aka 3% ’miivr‘. Q 3 (15 pts) 8. Given that the point (8, 6) is on the terminal side of positive angleei’n standard position. Draw this angle, using
a curved an‘ow from the initial side to the terminal side to indicate the direction of rotation. Compute exact vaiues (reduced ﬁactions) for the following trig functions of 9 . L.
. =:.% “g; X z a Is"
y M ( w) .7: ML 7 c: 4): 6" .5; C 4» (L9,, L. cscB: 3 = \iCa‘HM 6 ‘/ '3 i636 a 5*” 3 (6 pts) 9. In what quadrant does 9 lie ifthe following are true? a) sec6<0andtan6<0? Stine Mi SGC®<Géﬁ ank Q3
 \ C5669
os ivc: ..
{1) It +0;ij €45sz +CUMG<O~=§ QQOEQH
CoriG 8868' F7 f‘
b)9=2800° geometric 33’ E? Ww‘ilms "’ '3ng 13% 1530 320’ $ Q” (4 pts) E0. Find an angle a such that sees > 0 , but sec(6 — 2°) < O.
SecG» is positive ﬂu» Salt M52, Mgmh‘w V‘Uc Q 3 . Ans: WM °
So (PM sample. M .= 9N" . swam") o Moﬁeéma‘” m1
néiéﬁf 9°36: ’16?” : SQQQGQMO ....................... 3 “70° (8 pts) 1!. a) Given that 0° S 9 < 360°, ﬁnd all values for 3 such that 0089 = Sine. I o
CO5©2 .25». 0.. 9 Yb"): all['é‘LEC
 f" Gag “ " ‘3 1M ‘ H66
g u : l'éo
st = \:~, 5 X Y W“
(Sam 23)
13) Given that 0° 5 9 < 360° , ﬁnd all values for 3 such that (3089 = sect).
r  0 6
Cage): 3; Renewals» 0m. :21an «mi/‘1 WW  b) 02 i 86
r ibﬂ'i’im 3' i 5““ ”i '
$8693 "”' 5 ﬁ 0 o
X Cast) a Secc’b 7» l :30 o Ce$l85°=seel€l09= ”I 7““ (6 pts) 12. TRUE or FALSE N W Pﬁﬁﬁt at. S. i
2 l S E
a) There is an angle 0 in the ﬁrst quadrant such that COS 3 = 3 and Sin 9 = "3—, 3 g a) HALS E,
> Cos>€9+$u3©él '4 ‘ ‘3
3“? J. '3... m 1a» 2.. _.
(134’ s r q 4 q ¢l 7 6
b) Them 13 an angle 3 in the ﬁrst quadrant such that sin 9" —— ._ 6and 08(13— — 7. b) Flat. 3 E, Stine cmwlv ‘U—grewlu MI 6‘56 @ Whoiv @q ﬁg“ .?
c) 5609— — sec(3 + 1800"), for all non— quadrantal angles 6. GTE U: moo": s 360‘: so G+I%OO° is calamari to Q owl w.“
W 4&0. mm, shrug, values (Um»¢ua&m~i“~o\=b reeQ angels?) (8pts) 13 Solve for it so that the following are true statements. (Assume all angles are acute.)
1 3 mo =— 5x +31:
a) siu(3x + 40)° = Wm— (D =1 3% cse(5x+34)° 3
TN, Mus MLLiJf’ X b 3 a)— ibt quail. n ..
b) cot(2x—3)°tan(5x—1‘5)°ml 2X“: : 6 X is Ll
M (angt’ 2 MCSwS)" lx : Ex b)— Tiu. mix» Maul he. «null. (12 pts) 14. Use identities ﬁ'orn section 1.4 of your text (not xyr deﬁnitions) to ﬁnd the remaining trigonometric function values for quadrant 3 angle 9 in exact form, given that tan 9 = 3. Show all work clearly! Radicals should not be
approximated and may be left in the denominator. For an example of what I expect, refer to the handout from section 1.4.
The answers may be found in whatever order seems reasonable, as there are many different options. c) vi'aM‘GHesec‘Q ‘ _eu3JE’
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 Fall '09
 COHEN
 Trigonometry

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