SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Transcription

1 Math Pecalculus Ch. 6 Review Name SHORT ANSWER. Wite the wod o phase that best completes each statement o answes the question. Solve the tiangle. ) ) Two sides and an angle (SSA) of a tiangle ae given. Detemine whethe the given measuements poduce one tiangle, two tiangles, o no tiangle at all. Solve each tiangle that esults. Round lengths to the neaest tenth and angle measues to the neaest degee. ) B =, b =., a = 6.7 ) Find the aea of the tiangle having the given measuements. Round to the neaest squae unit. ) A = 7, b = 0 inches, c = 9 inches ) Solve the poblem. ) A guy wie to a towe makes a 67 angle with level gound. At a point ft fathe fom the towe than the wie but on the same side as the base of the wie, the angle of elevation to the top of the towe is 8. Find the length of the wie (to the neaest foot). ) Solve the tiangle. Round lengths to the neaest tenth and angle measues to the neaest degee. ) ) ) a =, b = 8, C = 0 6) Solve the poblem. 7) Two sailboats leave a habo in the Bahamas at the same time. The fist sails at mph in a diection 0. The second sails at 0 mph in a diection 00. Assuming that both boats maintain speed and heading, afte hous, how fa apat ae the boats? 7) 8) A painte needs to cove a tiangula egion 60 metes by 68 metes by 7 metes. A can of paint coves 70 squae metes. How many cans will be needed? 8)

2 Use a pola coodinate system to plot the point with the given pola coodinates. 9) (, - ) 9) - - Find anothe epesentation, (, θ), fo the point unde the given conditions. 0), π, < 0 and 0 < θ < π 0) Pola coodinates of a point ae given. Find the ectangula coodinates of the point. ) (-, 0 ) ) The ectangula coodinates of a point ae given. Find pola coodinates of the point. Expess θ in adians. ) (, - ) ) Convet the ectangula equation to a pola equation that expesses in tems of θ. ) x = ) ) 8x - y + 0 = 0 ) Convet the pola equation to a ectangula equation. ) = csc θ ) 6) = 8 cos θ + 9 sin θ 6) Pola coodinates of a point ae given. Use a gaphing utility to find the ectangula coodinates of the point to two decimal places. 7) -., π 9 7) Convet the pola equation to a ectangula equation. Then detemine the gaphʹs slope and y -intecept. 8) sin θ - π = 8)

3 MULTIPLE CHOICE. Choose the one altenative that best completes the statement o answes the question. The gaph of a pola equation is given. Select the pola equation fo the gaph. 9) 9) A) sin θ = B) = cos θ C) = D) = sin θ SHORT ANSWER. Wite the wod o phase that best completes each statement o answes the question. Test the equation fo symmety with espect to the given axis, line, o pole. 0) = cos θ; the pola axis 0) Gaph the pola equation. ) = + sin θ ) ) = sin θ )

4 Use a gaphing utility to gaph the pola equation. ) = - 6 sin θ ) ) = θ ) Gaph the pola equation. ) = - sin θ ) Find the absolute value of the complex numbe. 6) z = -0 + i 6)

5 Wite the complex numbe in pola fom. Expess the agument in degees. 7) i 7) Wite the complex numbe in ectangula fom. 8) (cos π + i sin π ) 8) Find the poduct of the complex numbes. Leave answe in pola fom. 9) z = (cos 7 + i sin 7 ) z = (cos 8 + i sin 8 ) 9) 0) z = + i z = - i 0) Find the quotient z of the complex numbes. Leave answe in pola fom. z ) z = 8 cos π + i sin π ) z = cos π + i sin π ) z = i z = i ) Use DeMoiveʹs Theoem to find the indicated powe of the complex numbe. Wite the answe in ectangula fom. ) (cos + i sin ) ) ) (- + i)6 ) Find all the complex oots. Wite the answe in the indicated fom. ) The complex cube oots of 7(cos + i sin ) (pola fom) ) 6) The complex fouth oots of -6 (ectangula fom) 6) Solve the poblem. 7) Let vecto u have initial point P = (0, ) and teminal point P = (, 0). Let vecto v have initial point Q = (, 0) and teminal point Q = (7, -). u and v have the same diection. Find u and v. Is u = v? 7)

6 Sketch the vecto as a position vecto and find its magnitude. 8) v = -i + j 6 y 8) x - -6 Let v be the vecto fom initial point P to teminal point P. Wite v in tems of i and j. 9) P = (-, 6); P = (-6, ) 9) Find the specified vecto o scala. 0) u = -i - 6j, v = 6i + 8j; Find u + v. 0) ) u = -i + j and v = i + j; Find u + v. ) Find the unit vecto that has the same diection as the vecto v. ) v = i ) ) v = i - j ) Wite the vecto v in tems of i and j whose magnitude v and diection angle θ ae given. ) v = 0, θ = 0 ) Solve the poblem. ) The magnitude and diection of two foces acting on an object ae pounds, N E, and pounds, S0 E, espectively. Find the magnitude, to the neaest hundedth of a pound, and the diection angle, to the neaest tenth of a degee, of the esultant foce. ) 6) One ope pulls a bage diectly east with a foce of 79 newtons, and anothe ope pulls the bage diectly noth with a foce of 87 newtons. Find the magnitude of the esultant foce acting on the bage. 6) 7) An aicaft going fom Atlanta to Savannah on a heading of (fom noth) is tavelling at a speed of 60 miles pe hou. The wind is out of the noth at a speed of miles pe hou. Find the actual speed and diection of the aicaft. 7) Find the magnitude v and diection angle θ, to the neaest tenth of a degee, fo the given vecto v. 8) v = -i + j 8) 6

7 Use the given vectos to find the specified scala. 9) u = -i - 6j and v = -i + 7j; Find u v. 9) 0) v = 6i + 8j; Find v v. 0) Find the angle between the given vectos. Round to the neaest tenth of a degee. ) u = -i + j, v = i - 6j ) Use the dot poduct to detemine whethe the vectos ae paallel, othogonal, o neithe. ) v = i + j, w = i - j ) ) v = i, w = -i ) Find pojwv. ) v = i + j; w = 8i - 6j ) Decompose v into two vectos v and v, whee v is paallel to w and v is othogonal to w. ) v = i + j, w = i + j ) Solve the poblem. 6) A peson is pulling a feight cat with a foce of pounds. How much wok is done in moving the cat 0 feet if the catʹs handle makes an angle of 6 with the gound? 6) 7) A foce of 6 pounds acts in the diection of 6 to the hoizontal. The foce moves an object along a staight line fom the point (6, 8) to the point (, ), with distance measued in feet. Find the wok done by the foce. Round the answe to one decimal place, if necessay. 7) 7

8 Answe Key Testname: CH. 6 REVIEW PRECALCULUS ) B = 7, a =.66, c = 6.7 ) A = 9, C = 8, c = 0.; A = 6, C = 6, c = ) 7 squae inches ) feet ) A = 8, B = 7, C = 7 6) c =., A =, B = 8 7) 90.8 miles 8) 7 cans 9) - 0) -, π - ), - ) 8, π ) = ) = cos θ -0 (8 cos θ - sin θ) ) y = 6) x + y = 8x + 9y 7) (-.6, -0.79) 8) y = x + ; slope: ; y-intecept: 9) D 0) has symmety with espect to pola axis 8

9 Answe Key Testname: CH. 6 REVIEW PRECALCULUS ) ) )

10 Answe Key Testname: CH. 6 REVIEW PRECALCULUS ) ) ) 7 7) 0(cos i sin 6.9 ) 8) - + i 9) 0(cos + i sin ) 0) cos π + i sin π ) 8 cos π + i sin π ) cos 7π + i sin 7π ) i ) -6 ) (cos 78 + i sin 78 ), (cos98 + i sin 98 ), (cos 8 + i sin 8 ) 6) + i, - i, - + i, - - i 7) u =, v = ; yes 0

11 Answe Key Testname: CH. 6 REVIEW PRECALCULUS 8) v = 6 y x ) v = -i - j 0) i + j ) ) u = i ) u = i - j ) v = -i + j ) F = 7.0; θ = -.6 6) 8 newtons 7) 69 miles pe hou; fom noth 8) ; 7. 9) 7 0) 00 ) 68. ) othogonal ) paallel ) - (i - j) ) v = (i + j), v = -i + j 6) 887. ft lb 7) 8.8 ft lb