NWACC Dept f Mathematics Dept Final Exam Review fr Trig - Part Trignmetry, 9th Editin; Lial, Hrnsby, Schneider Fall 008 Departmental Objectives: Departmental Final Exam Review fr Trignmetry Part : Chapters 7 and 8 7. Defining, using, and applying the Law f Sines and the Law f Csines. [Sectins: 7.1, 7., 7.] 8. Perfrming peratins with and applying vectrs. [Sectins: 7.4, 7.5] 9. Cnverting cmplex numbers int trignmetric frm & vice versa, perfrming peratins with cmplex numbers, and finding rts and pwers f cmplex numbers. [Sectins: 8.1, 8., 8., 8.4] 10. Cnverting between rectangular & plar crdinates and graphing plar crdinates and equatins. [Sectin: 8.5] Chapter 7: Applicatins f Trignmetry and Vectrs 1. Determine the remaining sides and angles f the triangle ABC. Shw all wrk and / r supprt yur answer.. Determine the remaining sides and angles f the triangle ABC. Shw all wrk and / r supprt yur answer. C = 71.8, B = 4.57, a =.614. A ship is sailing due nrth. At a certain pint the bearing f a lighthuse 1.5 km distant is N 8.8 E. Later n, the captain ntices that the bearing f the lighthuse has becme S 44. E. Hw far did the ship travel between the tw bservatins f the lighthuse? Shw all wrk and / r supprt yur answer. 4. Mark ntices that the bearing f a tree n the ppsite bank f a river flwing nrth is 115.45. Lisa is n the same bank as Mark, but 48. m away. She ntices that the bearing f the tree is 45.47. The tw banks are parallel. What is the distance acrss the river? Shw all wrk and / r supprt yur answer. 5. Find the area f the triangle ABC. Shw all wrk and / r supprt yur answer. A = 0.50, b = 1.00 cm, C = 11.60 6. A real estate agent wants t find the area f a triangular lt. A surveyr takes measurements and finds that tw sides are 5.1 m and 1. m, and the angle between them is 4.. What is the area f the triangular lt? Shw all wrk and / r supprt yur answer. 7. Determine the number f triangles ABC pssible with the given parts. Shw all wrk and / r supprt yur answer. a) b = 60, a = 8, B = 100 b) a = 5, b = 0, A = 40 c) B = 54, c = 8, b = 8. Find the unknwn angles in triangle ABC, if the triangle exists. Shw all wrk and / r supprt yur answer. a) C = 41 0', b = 5.9 m, c = 8.4 m b) B = 48., a = 890 cm, b = 697 cm c) B = 74., a = 859 m, b = 78 m 1
NWACC Dept f Mathematics Dept Final Exam Review fr Trig - Part Trignmetry, 9th Editin; Lial, Hrnsby, Schneider Fall 008 9. Slve the triangle ABC, if pssible. Shw all wrk and / r supprt yur answer. C = 5., a =.5 yd, c = 59.8 yd 10. Slve the triangle ABC, if pssible. Shw all wrk and / r supprt yur answer. A = 8 40', a = 9.7 km, b = 11.8 km 11. Slve each triangle and then find the area f the triangle. Apprximate values t the nearest tenth. Shw all wrk and / r supprt yur answer. a) b) 1. Slve each triangle and then find the area f the triangle. Shw all wrk and / r supprt yur answer. a) C = 8., b = 5.71 in., a = 4.1 in. b) a = 189 yd, b = 14 yd, c = 5 yd 1. The sides f a parallelgram are 4.0 cm and 6.0 cm. One angle is 58 while anther is 1. Find the lengths f the diagnals f the parallelgram. Shw all wrk and / r supprt yur answer. 14. A weight is supprted by cables attached t bth ends f a balance beam, as shwn in the figure. What angles are frmed between the beam and the cables? Shw all wrk and / r supprt yur answer. 15. Use the vectrs in the adjacent figure t find a) a + b, b) a b, c) a. Shw all wrk and / r supprt yur answer. 16. Find the magnitude and directin angle fr vectr v = 15, -8. Shw all wrk and / r supprt yur answer. 17. Vectr v has magnitude v = 15. 4 and directin angle a = 7 0 cmpnents f v. Shw all wrk and / r supprt yur answer.. Find the hrizntal (a) and vertical (b)
NWACC Dept f Mathematics Dept Final Exam Review fr Trig - Part Trignmetry, 9th Editin; Lial, Hrnsby, Schneider Fall 008 18. Write vectr v in the adjacent figure in cmpnent frm, a, b. Shw all wrk and / r supprt yur answer. 19. Given u =, 5 and v = 4,, find u + 4v. Write yur answer in the frm ai + bj. Shw all wrk and / r supprt yur answer. 0. Find the dt prduct f, - and 6, 5. Shw all wrk and / r supprt yur answer. 1. Find the angle between the vectrs -5i + 1j and i + j. Shw all wrk and / r supprt yur answer.. Given u =, 1, v =, 4, and w = 5, 1, evaluate u ( v w). Shw all wrk and / r supprt yur answer.. Determine whether the vectrs 1, and 6, are rthgnal. Shw all wrk and / r supprt yur answer. 4. A 10-lb frce keeps a 600-lb bject frm sliding dwn an inclined ramp. Find the angle f the ramp. Shw all wrk and / r supprt yur answer. 5. Find the magnitude f frce necessary t keep a 500-pund car frm sliding dwn a ramp f 5. Shw all wrk and / r supprt yur answer. 6. A ship leaves prt n a bearing f 4.0 and travels 10.4 miles. The ship then turns due east and travels 4.6 miles. Hw far is the ship frm prt, and what is its bearing frm prt? Shw all wrk and / r supprt yur answer. 7. A pilt is flying at 168 mph. She wants her flight path t be n a bearing f 57 40'. A wind is blwing frm the suth at 7.1 mph. Find the bearing the pilt shuld fly, and find the plane s grundspeed. Shw all wrk and / r supprt yur answer. 8. A pilt wants t fly n a bearing f 74.9. By flying due east, he finds a 4-mph wind, blwing frm the suth, puts him n curse. Find the grundspeed and airspeed. Shw all wrk and / r supprt yur answer. Chapter 8: Cmplex Numbers, Plar Equatins, and Parametric Equatins 9. Write 88 as the prduct f a real number and i. Shw all wrk and / r supprt yur answer. 0. Slve x + = 4x and express all nnreal cmplex slutins in terms f i. Shw all wrk and / r supprt yur answer.
NWACC Dept f Mathematics Dept Final Exam Review fr Trig - Part Trignmetry, 9th Editin; Lial, Hrnsby, Schneider Fall 008 1. Perfrm the indicated peratins and then simplify. Shw all wrk and / r supprt yur answer. a) 10 40 b) 1 6 8. Perfrm the indicated peratin and then simplify. Write yur answers in standard frm. Shw all wrk and / r supprt yur answer. a) ( 4 i) ( + i ) + ( 4 + 5i ) b) ( + i )( 4 i ) c) + i 1 5i. Simplify each pwer f i. Shw all wrk and / r supprt yur answer. a) 5 i b) 1 i 4. Write the cmplex number [cs 150 + i sin 150 ] in rectangular frm. Shw all wrk and / r supprt yur answer. 5. Write the cmplex number 5 5i in trignmetric frm r(cs? + i sin?), with? in the interval [0, 60 ). Shw all wrk and / r supprt yur answer. 6. Find each prduct and write it in rectangular frm. On part b, rund t fur decimal places. Shw all wrk and / r supprt yur answer. a) [ 8( cs00 i sin 00 )] [ 5( cs10 + i sin 10 )] + b) (1 cis 18.5 )? ( cis 1.5 ) 4( cs10 + i sin 10 ) 7. Find the qutient ( cs150 + i sin 150 ) & write it in rectangular frm. Shw all wrk and / r supprt yur answer. i 8. Cnvert the numeratr and denminatr f t trignmetric frm. Then find the qutient and write it in 1 i rectangular frm. Shw all wrk and / r supprt yur answer. 9. Find each pwer. Write each answer in rectangular frm. Shw all wrk and / r supprt yur answer. a) [ ] cis 100 b) ( i) 5 40. Find all cube rts f each cmplex number. Leave answers in trignmetric frm. Shw all wrk and / r supprt yur answer. a) 7 cis 00 b) i 41. Find all cmplex slutins f each equatin. Leave answers in trignmetric frm. Shw all wrk and / r supprt yur answer. a) x 4 i = 0 b) x 4 + 16 = 0 4
NWACC Dept f Mathematics Dept Final Exam Review fr Trig - Part Trignmetry, 9th Editin; Lial, Hrnsby, Schneider Fall 008 4. Fr each pair f plar pints, plt the pint; give tw ther pairs f plar crdinates (including ne with a negative r); and give the rectangular crdinates fr the pint. Shw all wrk and / r supprt yur answer. 5π b), a) (, 15 ) 4. Given the rectangular crdinates 1,, give tw pairs f plar crdinates fr the pint, including ne with a negative r. Select? s it is in the interval [0, 60 ). Shw all wrk and / r supprt yur answer. 44. Fr each rectangular equatin, give its equivalent plar equatin and sketch its graph. Shw all wrk and / r supprt yur answer. a) x y = 6 b) x + y = 9 45. Identify the type f plar equatin and draw a cmplete graph. Shw all wrk and / r supprt yur answer. a) r = + cs? b) r = 4 cs? 46. Fr each plar equatin, give its equivalent rectangular equatin and sketch its graph. a) r = sin? b) r = 1 sin? Answers Chapter 7: Applicatins f Trignmetry and Vectrs 1. A = 7., a = 178 m, c = 44 m. A = 65.60, b = 1.94 cm, c =.77 cm. 7.8 km 4. 9.4 m 5. 65.94 cm 6. 7 m 7. a) 0; b) 1; c) 8. a) B 6 0', A 11 10'; b) A 1 7., C 1 59.6, A 107.8, C 4.0 ; c) n such triangle 9. A 5.5, B 10., b 7.9 yd 10. B 1 49 0', C 1 9 00', c 1 15.5 km, B 10 40', C 10 40', c.88 km 11. a) A., B 108., C 49.5 ; area = 1 15.units b) A 56.7, C 68., b 88.; area = 1547079 680.6 units 1. a) c.8 in., A 44.9, B 106.8 ; area = b) C 107 0', B 9 00', A 40'; area = 1. 5. cm, 8.8 cm 14. 6.4 and 6..5688517 5.7units 7645000 1904.0 units 5
NWACC Dept f Mathematics Dept Final Exam Review fr Trig - Part Trignmetry, 9th Editin; Lial, Hrnsby, Schneider Fall 008 15. a) 0, 10 b) 8, c) 4, -6 16. v = 17 ;? = 1.9 17. a 1.7, b 7.11 18. v = 4, 4 19. 0i + j 0. 1. 78.9. 4. rthgnal 4. 1.5 5. 05 lbs 6. 1.5 mi; 50.4 7. bearing: 65 0'; grundspeed: 181 mph 8. grundspeed: 161 mph; airspeed: 156 mph Chapter 8: Cmplex Numbers, Plar Equatins, and Parametric Equatins 9. 1 i 0. x = ± i 1 1. a) i b) 1 1. a) 10 + i b) +16i c) + i. a) i b) i 4. + i 5. 5 ( cs5 + i sin5 ) 6. a) 0 + 0i b) 0.8580 + 18.5414 i 7. i 1 8. i 7 7 9. a) i b) 18 + 18i 40. a) cis 100, cis 0, cis 40 b) ( cs 110 sin 110 ) + i, ( cs 0 sin 0 ) ( ) i cs 50 + i sin 50 +, 6
NWACC Dept f Mathematics Dept Final Exam Review fr Trig - Part Trignmetry, 9th Editin; Lial, Hrnsby, Schneider Fall 008 41. a) cs.5 + i sin.5, cs 11.5 + i sin 11.5, cs 0.5 + i sin 0.5, cs 9.5 + i sin 9.5 b) cis 45, cis 15, cis 5, cis 15 4. a) (, 495 ), (, 15 ), (, ) p 4p b),,,,, 4. (1, 10 ), (-1, 0 ) 44. a) 6 r = b) r = r r = cs? sin? 45a. 45b. 46a. 46b. 7