4.1.1 Angles and Ratios Worksheets - 2 BS l0 11 C12 Lill Exercise You may express answers for trigonometric values in fractional or radical form TRlG

4.1.1 Angles and Ratios Worksheets - 2 BS l0 11 C12 Lill...

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Unformatted text preview: 2 BS l0 11 C12 Lill Exercise You may express answers for trigonometric values in fractional or radical form. TRlG RATIOS AND ANGLES lN STANDARD PDSlTlDN For each angle, a point 0n the terminal arm is shown. Calculate the primary trigonometric values. ' (bl -" A point on the terminal arm for each angle is shown. Calculate the reciprocal trigonometric values of each angle. (a) (b) .v (C) 5‘ U V (—7, 24\ I ~ :1 EJI‘ O ‘ 55—11 rot §¥=a UL‘I‘—%=9W —+= Quart!!!) (—24.—10l I) E; :gum‘g: =gsoo‘%=9uts(ztt)%+ =9urzt O . E = 9 son if = 9 Uisultq Fries!) 9W1.) fluxes 8 :91.“ Ll . ———-Ql£)3——=93‘QS -—-——= URI—=QS'OD Sl Ll 8 S! The point P(2, 7) lies on the terminal arm of 9. For 6, find the .Lt _ _ 9 quts L = x, m .vz __ n 335. L ___ n 353 (a) sine (b) cosine (c) tangent 8_ .- 1‘73 SZ 5‘ ‘_ ‘E=DUE)‘é—€:DSOD(Q_£-=9103’-:§——=9353 The point Q(—9, ll) lies on the terminal arm of a. For at, calculate its L _ V H H ““1 ue EJ— soa ‘Si 2 urs(z‘ (a) cosecant (b) secant (c) cotangent "g“: 9 l “a " = 9 g " 9. " 8 ll ’ 3 _ _..tTLr—=gsso‘?§fl—=gsoa(qg/x=goas (a) Angle 9 is a second quadrant angle, and cos 9 = —-. Sketch a diagram. 5/\ - 3 gr 4 ‘ Z _ 9 urge-L ‘9‘ \_ )0 He] ‘l9l _ = Duis(q (b) Find the other primary trigonometric values of 9. g _' .37 .5 3 .1; = 9103 E” = g ass ‘E— = 9353(8'9 (a) Angle 9 is in the third quadrant and'tan 9 = Z. Find the reciprocal .5... = 0 net ;_l7__ = 9 “((1.5 l_l___ = ,0 103(3) trigonometric values. L_/‘ U‘ i 6 E (b) A l . . l f d __ 8 F. l __6.._._ = D 333(q H = D 353(2‘}; EC) gm ng e at IS to he ourth quadrant an cos ix — TE. ind tie other zozfx ZOZA L z trigonometric values " if} pg L ’17: - 1 L (3-: L = 9103 ‘SZ _ g 325 3?: _ 9 333(1) 9 ' h t d . = —-,_- ‘ . (a) is a rs qua rant angle llcose J5, find sm 9 and sect? . _t%_ = g ‘03 E1?" = 9 333 {g = 0 asap EST _ 9 ‘03 . _ 7 _, ' ‘21 s E _ ‘v = (b) [3 is a second quadrant angler If tan [3 = [6? find cos [3 and csc B. 6-— = 9 395 fi- = 9 393m 3— D ‘03 E— 70 335 _ .. ‘2 =Iooso(e‘z Q—=guai‘ ‘fl_ =9soa Draw a sketch of each angle in standard posrtron. Calculate the other 9 9 ll trigonometric values of each angle. is. = 9 Ulstll is? = 0 um %_ __. 9 so: 13 , 7 17 (a) sec9 = —E’ (b) srna2i—5, (c) csc9 = ‘f’ p .573“ = QUESCB ?_ = Qua, 1% = 9503 9 in third quadrant a in first quadrant 9 in fourth quadrant {I it ‘ I ‘-§—- = guts“ -—g— = 9 um Z—l = 9503 '9. = 9u!5(9 Plx, y) is a point on the terminal arm of or. OP = r. t C c g . . . - — “ ‘1 h (a) Fund the possrble values oflt in each of the followzng. { H9 2‘7}; =59 375‘“ “NP — — — 6 ”‘31 (b) Find the primary trigonometric values for each value of k. g g t. __ l7_ .9 , .. = 9 5° =9 “ESQ T gum — = 9 503 (1) PG, k). r = 5 (n) P(k, 8), r = 10 . (1n) P(3, k), r = 413 17 '5 h v ' ‘2 ~ 7 - . '§=9u15(q——:9ug] fl- SODH—E—l UlS As to algebra, srn or means (Sm a)‘. on IS a {bird quadrant angle and E Zl S ' 9 r = 9 (g I 5 - - 7 t ' I A i iiii ‘asrzuaxg tan or = ~13 Find a value for sun1 a +,cos* a. .. 17 B IS a second quadrant angle and csc t? = E. Find a value for 25inB+3cosfi. For any angle 9, show why l l l ‘ e = __.~.. = = _ (a) sm csc 0 (b) cos 9 sec 9 (c) tan 6 cot 9 l l d e z _ = = ( ) CSC sin 9 .(B) sec 9 cos 9 (f) CO: 8 tan 8 81 61 9 395 (D) 19131: = 9800 (2) ‘asuz; 9m Bugmonol “9‘11 M0118 9m 30 11:)ng ‘samaA ognawouofign )0 53mm 9m 01 Eupmej momgm 021790 = 92: ugs (12) 1912‘s IZEL'1 = (HZ — 906N191 (3) J79 U15 5’5 oZE “15 Z (2) 512010 = (.01 + (1)803 (q) 319 pug “91-171 ‘006 > 9 > 00 .11 9 5 00 Jo} = 9 “93 (‘11 > eoz U35 (q) 1913 = 9 U15 (9) 1§IZ'E 1.09 “15 ¢ 0017 “15 ‘1' (3') 191:1 = 9 050 1.1) ISIZ'E = 9100 (0) 'SJQMSUE anK JO} 911031391 9A19 L506 E 5/. U131 :52 U9] 95 —0.6691. —O.4695. cos 9 = 43.8829 (an 6 = 0.5317 c)sin H = —0.5299. cos 9 = 0.8480. For0° g a 5 90°. .a)10" b)74° C)15° Q48" m4?" e)52° f)51° 5.a)O_.9205 . cos 6 s 1 20 10.8)27" b)34° c)37" d)74° 11.3)30“ 1.048" c)56" (an 9 = 416249 d)sin 6 = 0.9703, cos 9 = -0.2419. d)37° 12.3)10“ M13" 036° d)78° 365° 1325" 1.a)O.7314 b)1.1106 61.4142 (90.6428 (2)1466} (an 0 = ~4.0108 9.a)——O.9336 b)0.4245 c)-—-3.8637 01.0000 g)1.2361 h)0;7431 110.6157 j)0.7986 100.7813 1)1.2868 2.3)1 b)D c)I (DD e)1 DD g)20° h126° i)73° 13.3)155° b)209° c)240° d)275" 8155" f)211° 14.b)245°. 295° 15.2)110", 250° b)155°. 335° 16.20243". 297° b)22°. 3385431031" 283° d)116°.244“ e)15°. 195° 058°.122‘ I7.a)1 b)D ()1 d1D e)[ f)D 18.(a). (c): g)6.3133'h)0.8192 6.3)0.7986 b)0.0349 C)O.7071 O s sin 6 3.8)49" b)49° c)50° (1)48" e)52° 054° 4.3)48° d)1.1504 e)-0.7071 f)!.8361 g)2.9238 107.1154 b147° b)0.7193 (35.2408 d)1.0187 e)1.1223‘ 00.3249 7.3)S9° b)-304° 8.a)sin 6 = 0.7431. cos 8 tanl? = ~1.1106 b)sin6 4.5 Exerci'se, page 158 a 60 E meow E .008 i m as E a moo 3v m Em E 3 3:2: 5 umséu 2: Brian $28.55 m E 6&5 E2253 Ea x mm m E m: n a 30 CV $3.0 H a :5 E vwmvdl H a m8 2: EM?! n e E: E $8; “zoom By 2331 n «:5 3 zoom We W so $53028 2: .o :2; he a be $33, “Eamon 95 SE 2 83.0.. n a E: E 83.01 n Q m8 E .202” W e W ...o .m .0 82?; m 2: vac “Em mEEwED up: 350 n— .uoom W a W ..o .2 27¢ 34 42.9.33 some 5 :oEwou 63.2..me E a 2.95 2.: 5285 A5 .Emzw Efivmsc 5:28 .6 2:: 1. 85:0 3 a :2: 33mm»: 2 e Em 85m .3361 u a Em 303% .1 E Ema: u my m8; E E: n 33 E a $3.01 u a E E _: 22.7 “33 E .E 32.0 n a E: An: : ~60de u a moo 3 wow». W a W co 5 ._o ”29, 3: 3E .cofim 2 E532: up: 6 some Em 2 m3 2 u a 8m 7:. omvmd N a Em a. $3.0 H a you E 3.8; n a 80 AB Smog u a 03 A3 32.0 n a Em E .mEBoze 2: go some t: a 02:; 2: EE ES 1:8 3 3:.” n a so a 32.0 n a 52 E m: mn u mu 8:3 minis 7138:; m is: m a d , .m B 03.; sumo UEL 2mg E8923 3.5 m 2 a 2 ENE E 34.: E 32 E : in E .832“. :23: 2: .2 a EE .2 .6 EE BEES“ 2: co ESQ m m_ 2. in 9 E : 5...“. E .5397. c .c 03$ umbqucowE 2: can .EEwEn :23 EL 9 s .o 35:; ucBEocowE 32:5 of :a 23:28 8 5.:me 55 3 52:585. up: 33 w 2: . .,. E @5323; 2: be some 5.. a .6 02? 2: 2E N. m {mica E cm: ”8 E .238 E .E 5m E .._o 2:? 2: EC. 0 32 98 n: b.2128 E E: 1:8 E as as E .a as 3 ate g .3 as E .E 8“ E .3 E E .2 m8 3 .w:<>o=£ 2: go gum» .3 2:? E: warm .3 E E D: B” E ‘4') ~82 u m as E 38.0 n m :5 E is: u m 03. E 33 n a E E .3323 2: Ho 63 E m Em v 05.0 u m m8 Q 3...? n w 08 E 2&3 n m 3m E 33.0 u m m8 E 3m: u m as E 32 n a 5m 3 .mEBo=£ 05 .8 :03 p8 w uni m 98% u m. 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  • Spring '15
  • quadrant, trigonometric values, primary trigonometric values

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