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c"+*'"" 'cW(L, I 1 t"-;*-< :,-!-w.,.%._- ,isroi. \ '* .111-t \tlr,/. t t I \- -*r5t. t-trr ,€D ---\ /lroff 6-l\ T ,P.) &,'% ,r*|nk ! d3 w" .'..."r*-- &,9t ,li i 'nltr G,7 (ffi,4-- EI , s&t r l>,2) ?-) -* t9. ,/ L} , -?j 6f 2, b) .a '' t I/ I .i t r'-'iW -'1,.- n' Ll- .,''/ t' [ *r\-**t,, -- .." / ,',' I / | \ " -JX \ t ,8.,, /,ri -fe LE, e) -'. &,'5 a {os;l-'v I ta nn J.;t 2) Do the following for the angle, 0 = -7n/3, C{rCWrl;SL a) Sketch the angle in standard" position.,, "":Vli'le -ry b) -. n lL @ 3 Determine the quadrant in which z -'1. Q ro -r7u#'- - -t1?,,0o fv W 3) ,W tr- b) c) Determine the quadrant in which the angle lieq. 1 W;rr /7 Drl -/tt 7,t-< Determine one positive and one negative coterminalangle forthe given angle, in both degrees and radians. /4( 27 t4 % 4) Convert the following angle measure from degrees to radians. 450o //fo, 5) Convert {fu2 W=,ffi 6) the following angle measure from radians to degrees.Ztl/Ls Find the le ngth of the a rc (a rc length) on a circle of radius 3 meters a nd interce pted by a centra angle of 1"50". kr c le n6U lta 5;rs [' J-- g*f rc") o I -{A , -!L / F- fo" %' I ? ,f {n -{n* 4cl 7) Find the radian measure )r rf Ine the cenu r ntra length 7 feet, I a ngre or a circre :,^"1,':-{-7,)," pts an arc of f roJ"olJ 6 fO $r 1t L. ,ty\rs 7 W , ll'P 1P+TftM It Pl- ,*?, /4 r /4 :* : l( -- ?.t 8) ffi'bl?-t', rei Phonograph records are vinyl discs that rotate on a turntable. A typical inches in diameter and plays at 33 1/3 revolutions per minute. a) What is the angular speed of a record album? b) What is the linear speed of the outer edge of a record album? b) rd album is 12 3Tcql' JT rcA h.,^ -lffiokt,o" wA WW,L6 ut l-rtn1,L-( lfVoL -- h'*e t/n /rn)A 9) Find the area of the sectorof a circle of radius 6.5 millimeters and centralangle ft= *r"* k-- /{oo iC*.f( Y) 1tn46 (os t ,lt +a^Wn -* 1frY5 11) Evaluate (if possible fns-tfi=* @ -Lt2- 'J -] I srn( 'n al - '-' IJ- G =-F;g'i,lq --J?/ I tric functions at the given real number, ',L t = -4n/3. (lrr*U tO Jc*4r l--ry '- ^ J A**rCl*ckbtt I t = sinlTr/4 5in tE t -@ l"- 12) Evaluate the trigonometric function using its period as an aid. r{ ,iF 4./ {@ 5'q FE=-tr h'-h -A:{'ry r,l'{' ;: t='r Q y Tl . =PT lToo tto r'' 41 5; 4 l? a .tL"-T Sln'W,G r y r {e D._3 "_LA -*rr' 150o. arat a3[ - 6U /, UTZl1 b- i*'2, -h+'+ : hzrr{qn)rk *; tfut&r/n,^'[tZ ) 10) Evaluate (if possible) 0 r%)= }i"p!+T =js n ,tr e- 8O -6{1 ^4 t43 1-3) Evaluate the trigonometric function using its period as an aid. cos(-132l3) -a) dst S,tn tq ,5;^ /uq) )= =Si^/zztt{ Ssn 33= ? 15) Use the value of the trigonometric function to evaluate the indicated functions. (t(t, f sin(-r) = 3/B a) sin t b) csc t 5;nL I g t3 Stng = I -tt'- -2a / 3 ff1:, C*H)= Cost ,[fl t{\ 1 lll["?,, Serk)r H ,zT-e=66, 16) Use the value of the trigonometric function to evalu ate the indicated functions. \?y COS \,r )' ot c) d) cos(z+r] . \ Lt^ (^ (rr-t)= -'s J*. { [^(n+t)= -+ L7) Use a calculator to evaluate the trigonometric funct ion. Round your answer to four decimal places. Make sure the mode in calculator is on radians. (nsU a) cscZrf3 b) cos (-1,7) c) cot (-0.9) )f, <Z 6'^4 v -'-rlr 2- t{rndu,[oJ'n"ns W,Y I L/ 3 (o l. 154 1 r \_ ,) 4),4) - 46 E 18) Find the exact values of the six trigonometric functions of the angle shown in the figure. fuLo = {,7,'* =i=ry ?i!y=*'ffi, ', ,zz # ,. _l I x to*f' ,:_ 6r( *t(o Lb t41 :E ryiF ,fr r:1, r ff'r+= +=3 ffi ,t ktl > s, ;ff"8 x'fl ' yr>f= , rr7,2[L&o'i=iftl3 J)nt= = v r vat ue of the trigonometric fu nction to evaluate the indicated functions. ll',.*i" / ;,;.; ovb-# = tl 7 g=#,,{=T31, LHv;:r* -lJ 1sCI= ,)* -liTt' 7-. .L e,l-a19) usltne r+/' 5rn til3 t ,+, fI - e L r= x" (rrt=s=@' ', I 3lr -$^T L I l'3 i -B e, eG 3G v 4 *' ?/ =fi=ffi (o,)C L-t' s*&=ff-,rf=fr'fr uY'u Crtb & ;4-_ 3,ffi2 r 20) lfrl *':'" ofutfi/et{gonomelric function to evaluate the indicated "lt'fi 1*H':" r''' fu/u -i\ Use the value |" "' "' ^'u" yy,h i' ::i4,"-, oyq,y I r'-l rr d't er- I ^'r: I functions. ns runc'l' :E f, fu,tbI,#*/9 n L |; fft: '*i,-,'i b- l>2tl b ,/, v L btn ff= -r 2t) h0= LI f.Co5o =A Using the triangle above, verify/prove the following Pythagorean Trigonometric ldentity: X"t?'= rL sin20+ cos2e=7 ;fL n)o Ji^ r' (r'coso)" l- ( (> f'(os'? f fs;n's ( L S; J_q (u (osLa 22) C" (" /'|;n't L = I Find the exact values of the six trigonometric ratios of the angle 0 in the given triangle. ?" E' v'.t WY Y'+ Y', t{ 1 f,no=N fi0 fo}*: -rr'- r G 1{v -'- -'X W: 7"/ r ws ta 4-- u -- tw.-zyk- 1k V;,G e'--- (( W: bl cyft= M= fuLot &l-g; W__ ffi, S,Fr- L 't{ '[^(f _-r t- L 1 -a ,l;r 4-D €l V - 7,trr €r- r{ 7 w. ,kr 23l. Find the exact values of the indicated variables. 5r,.. 4to= tr, = $in+t' : -! 0s ?r u 28 S;notf,a= x 1-. h't0rn)' Pt =28 kLtr lf6't = Tttt y'+ sq L -- 18'( I = + ry P x -\ y fr (ot?fo: 2t . tlAe* ^k 4 Sketch a triangle that has acute angle 0, and find the other five trigonometric ratios of 0. a) cos0 = 9/40 b) tan1 = fi c) cscO = 13/72 Cao qX ' 4of --l-- ar 4 quu';'(oL Y 8t lf;lboa lsn uLl-,Y=,1st4 Art n X=,ffi 24) Nf- k -tse (a /r', k f, t,t,6- k'= 3( e7 ZV 25) Evaluate the expression without using a calculator sln30ocsc30o a/ 26) LL 2;ft-l 7t 7 i.--J a\ ./ Evaluate the expression without using a calculator (sin 60")2 * (cos 60)2 ($,+U)" fru 27ll *:1;n Evaluate the expression without using a calculator (l))L., 6'" t;1'"'(;) - "'(1)'"' . rq *-/4 L). 2- * ,')" (@) Gn qY=[+) ' 7 _-- d- 4 q" e 6-@= I -L,fi- "% f-qls = betweenf, pole is the wire'and the ground is 52o. How far from the base of the: Pure 15 the wrr tr dtLcrLIrtru Lrr= wire attached to LU the Lrrtr . :@ ,,tz) ground? Assume the pole is t/a' -lb 28) A guy wire runs from the ground to the top of a 25-foot telephone pole. The angle formed lans)o'? l^\u =ffi ,'l trx ^ -non- = ry- i? X,ttnfio;9'{ } /'/;2{ tln;?o 14,;Fr 29) A 20-ft ladder leans against a building so that the angle between the ground and the ladder is72'. h 5in 1g,o - -h >o 2a,5ta ?)o 30) uh From a point on the gro u nd 500 ft from the base of the build ing, a n observer finds that the angle of elevation to the top of the building is 24o and that the angle of elevation to the top of a flagpole the height of the building and the length of the flagpole. llonLl- otr PnlC l^ - 1-. 9-1'=E {oct ;E E Y Sn(o rqt) {ao l^nn )10 K \, W7YT N