Chapte 7-8 Review Math 1316 Name SHORT ANSWER. Wite the wod o phase that best completes each statement o answes the question. Solve the tiangle. 1) B = 34.4 C = 114.2 b = 29.0 1) Solve the poblem. 2) Two tacking stations ae on the equato 163 miles apat. A weathe balloon is located on a beaing of N 43 E fom the westen station and a beaing of N 17 E fom the easten station. How fa, to the neaest mile, is the balloon fom the westen station? 2) 3) An aiplane is sighted at the same time by two gound obseves who ae miles apat and both diectly west of the aiplane. They epot the angles of elevation as 14 and 21. How high is the aiplane? 3) Find the aea of tiangle ABC with the given pats. Round to the neaest whole numbe. 4) A = 26.4 b = 12.3 in. c = 7.7 in. 4) Solve the poblem. ) Find the aea of a tiangula-shaped field with sides of 17.4 m and 226.7 m, and the included angle between them measuing 79.27. Round to the neaest squae mete. ) Find the missing pats of the tiangle. 6) B = 42 30ʹ b = 8.67 a = 21.01 6) 7) B = 11.4 b = 10.38 a = 26.26 7) Solve the poblem. 8) A ship sailing paallel to shoe sights a lighthouse at an angle of 10 fom its diection of tavel. Afte taveling 3 miles fathe, the angle is 21. At that time, how fa is the ship fom the lighthouse? 8) Find the missing pats of the tiangle. 9) C = 116.7 a = 7.0 km b = 9.80 km 9) Find the missing pats of the tiangle. (Find angles to the neaest hundedth of a degee.) 10) a = 6.1 in. b = 13.6 in. c = 16.0 in. 10) 1
Solve the poblem. 11) Two points A and B ae on opposite sides of a building. A suveyo chooses a thid point C 77 yd fom B and 103 yd fom A, with angle ACB measuing 8.9. How fa apat ae A and B (to the neaest yad)? 11) 12) Two aiplanes leave an aipot at the same time, one going nothwest (beaing 13 ) at 414 mph and the othe going east at 33 mph. How fa apat ae the planes afte 4 hous (to the neaest mile)? 12) Find the aea of tiangle ABC with the given pats. Round to the neaest whole numbe. 13) a = 17.4 cm b = 1.0 cm c = 13.4 cm 13) Solve the poblem. 14) A painte needs to cove a tiangula egion 64 metes by 67 metes by 73 metes. A can of paint coves 70 squae metes. How many cans will be needed? 14) Daw a sketch to epesent the vecto. Refe to the vectos pictued hee. 1) b + c 1) Use the figue to find the specified vecto. 16) Find a + b. 16) Find the indicated vecto. 17) Let a = 3i, b = i + j. Find 4a - b. 17) 18) Let a = -, -1, b = -3, 6. Find b - a. 18) Find the magnitude and diection angle (to the neaest tenth) fo each vecto. Give the measue of the diection angle as an angle in [0,360 ]. 19) -12, 19) 20) -8 2, -8 2 20) 2
Vecto v has the given magnitude and diection. Find the magnitude of the indicated component of v. 21) α = 9.3, v = 79.9 21) Find the hoizontal component of v. Wite the vecto in the fom <a, b>. 22) 22) Two foces act at a point in the plane. The angle between the two foces is given. Find the magnitude of the esultant foce. 23) foces of 2.0 and 31.8 lb, foming an angle of 162.8 23) Use the paallelogam ule to find the magnitude of the esultant foce fo the two foces shown in the figue. Round to one decimal place. 24) 24) Find the component fom of the indicated vecto. 2) Let u = -4, -3, v = -9, -1. Find u + v. 2) 26) Let u = -9, -9, v = -3, 3. Find -u + 9v. 26) Wite the vecto in the fom ai + bj. 27) -2, 8 27) Find the dot poduct fo the pai of vectos. 28) -10, 8, 4, 13 28) 29) i + j, -13i - 8j 29) Find the angle between the pai of vectos to the neaest tenth of a degee. 30),, -3, 8 30) 3
31) 7i - 4j, 2i - 8j 31) Solve the poblem. 32) If u = -3, and v = 4, 4, evaluate (2u) v. 32) 33) If u = -, 3, v = -, -6, and w = -3, 12, evaluate (u + v) w. 33) Detemine whethe the pai of vectos is othogonal. 34) -2, 6, 11, - 34) 3) 3, 9, -6, 2 3) Solve the poblem. 36) Two foces of 626 newtons and 170 newtons act at a point. The esultant foce is 691 newtons. Find the angle between the foces. 36) 37) A plane is heading due south with an aispeed of 264 mph. A wind fom a diection of 9 is blowing at 13 mph. Find the beaing of the plane. 37) 38) A pilot wants to fly on a beaing of 6.3. By flying due east, he finds that a 0-mph wind, blowing fom the south, puts him on couse. Find the gound speed of the plane. 38) 39) Two foces, of 6.7 and 44.1 lb, foming an angle of 83.2, act at a point in the plane. Find the magnitude of the esultant foce. 39) 40) What is the minimum foce equied to pevent a ball weighing 26.7 lb fom olling down a amp inclined 32.3 with the hoizontal? 40) 41) A foce of 3 lb is equied to hold a 72 lb toolbox on an incline. What angle does the incline make with the hoizontal? 41) 42) A fishing boat leaves pot on a beaing of 3 and tavels 13.3 mi. The boat then tuns due east and tavels 4.0 mi. How fa is the fishing boat fom pot, and what is its beaing fom pot? 42) Wite the complex numbe in ectangula fom. 43) 8 cos π 6 + i sin π 6 43) 44) 6 cis 13 44) Wite the complex numbe in tigonometic fom (cos θ + i sin θ), with θ in the inteval [0, 360 ). 4) -1-20i 4) Find the poduct. Wite the poduct in ectangula fom, using exact values. 46) [7(cos 4 + i sin 4 )] [2(cos 90 + i sin 90 )] 46) 4
47) [4 cis 300 ] [ cis 120 ] 47) Find the quotient and wite in ectangula fom. Fist convet the numeato and denominato to tigonometic fom. (cos 200 + i sin 200 ) 48) 48) 4(cos 0 + i sin 0 ) 49) 2 3 + 2i 3 - i 49) Pefom the indicated opeation. Give answes in ectangula fom expessing eal and imaginay pats to fou decimal places. 0) (12 cis 14. )(3 cis 8. ) 0) Find the given powe. Wite answe in ectangula fom. 1) (- 3 + i)6 1) 2) 4 cis 1 4 2) Find all cube oots of the complex numbe. Leave answes in tigonometic fom. 3) -12i 3) 4) -8 4) Find all specified oots. ) Fifth oots of 1. ) Find all solutions of the equation. Leave answes in tigonometic fom. 6) x4 + 16 = 0 6) Plot the point. 7) -2, -π 4 7) - -
Give the ectangula coodinates fo the point. 8) (, 330 ) 8) The ectangula coodinates of a point ae given. Expess the point in pola coodinates with 0 and 0 θ < 360. 9) (2, -2) 9) Detemine two pais of pola coodinates fo the point with 0 θ < 360. 60) (-2 2, -2 2) 60) Fo the given ectangula equation, give its equivalent pola equation. 61) 2x + 3y = 6 61) Find an equivalent equation in ectangula coodinates. 62) = 10 sin θ 62) 63) = 1 + cos θ 63) 64) sin θ = 10 64) The gaph of a pola equation is given. Select the pola equation fo the gaph. 6) 6) 6 4 3 2 1-6 - -4-3 -2-1 -1 1 2 3 4 6-2 -3-4 - -6 6
Gaph the pola equation fo θ in [0, 360 ). 66) = 8 + 8 sin θ 66) 67) = sin 2θ 67) 68) = (1 - sin θ) 68) Find the pola coodinates of the point(s) of intesection of the given cuves fo 0 θ < 2π. 69) = 3, = 3 + sin θ 69) 70) = + 3 sin θ, = + 3 cos θ 70) 7
Answe Key Testname: TRIG CH. 7 8 REVIEW 1) A = 31.4, a = 27.20, c = 47.63 2) 36 mi 3) 3.6 mi 4) 21.1 in.2 ) 19,34 m2 6) no such tiangle 7) A1 = 30, C1 = 138.6, c1 = 34.73; A2 = 10, C2 = 18.6, c2 = 16.7 8) 2.73 mi 9) c = 14.8 km, A = 26.9, B = 36.4 10) A = 21.92, B = 6.34, C = 101.74 11) 91 yd 12) 2771 mi 13) 97 cm2 14) 29 cans 1) 16) -, 11 17) 11i - j 18) 2, 7 19) 13; 17.4 20) 16; 22 21) 40.8 22) -8.43, 7.07 23) 11 lb 24) 146. lb 2) -13, -4 26) -18, 36 27) -2i + 8j 28) 64 29) -10 30) 6.6 31) 46.2 32) 16 33) -6 34) No 3) Yes 36) 74. 37) 182 38) 120 mph 39) 7.8 lb 40) 14.3 lb 41) 29.1 42) 1.9 mi; 46.9 43) 4 3 + 4i 44) -3 2 + 3i 2 4) 2(cos 233.1 + i sin 233.1 ) 8
Answe Key Testname: TRIG CH. 7 8 REVIEW 46) -7 2 + 7 2i 47) 10 + 10 3i 48) - 3 + 8 8 i 49) 1 + 3i 0) 33.1382 + 14.0663i 1) -64 2) 128 + 128 i 3 3) cis 90, cis 210, cis 330 4) 2 cis 60, 2 cis 180, 2 cis 300 ) 1, cis 2π, cis 4π, cis 6π, cis 8π 6) {2 cis 4, 2 cis 31, 2 cis 13, 2 cis 22 } 7) - 8) 3 2, - 2-9) (2 2, 31 ) 60) (4, 22 ), (-4, 4 ) 6 61) = 2 cos θ + 3 sin θ 62) x2 + y2 = 10y 63) y2 = 2-10x 64) y = 10 6) = 4 cos θ 9
Answe Key Testname: TRIG CH. 7 8 REVIEW 66) 16 12 8 4-16 -12-8 -4 4 8 12 16-4 -8-12 -16 67) 10-10 - 10 - -10 68) 10-10 - 10 - -10 69) (3, 0), (3, π) 70) + 3 2 2, π 4, - 3 2 2, π 4 10