MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Transcription

1 Test # Review Math (Pe -calculus) Name MULTIPLE CHOICE. Choose the one altenative that best completes the statement o answes the question. Use an identit to find the value of the epession. Do not use a calculato. ) sin.7 csc ) Find the efeence angle fo the given angle. ) ) Use a vetical shift to gaph the function. ) = + cos )

2 Gaph the function. ) = csc )

3 Complete the identit. ) tan (cot - cos ) =? - sin 0 - sec ) Find the eact value of the epession. ) cos π sin π - cos π π sin ) Use the given infomation to find the eact value of the epession. 7) Find sin θ. cos θ = 7, θ lies in quadant IV. 7) Use a calculato to solve the equation on the inteval [0, π). Round the answe to two decimal places. 8) tan =..,.7.,.9.,.00.,. 8) Solve the tiangle. Round lengths to the neaest tenth and angle measues to the neaest degee. 9) A = B = a = 9.8 C =, b =., c = 8.7 C =, b = 8.7, c =. C =, b = 8.7, c =. C =, b =., c = 8.7 9)

4 0) 0) 7 A = 8.8, B = 8., C =.8 A =.8, B = 8., C = 8.8 A = 8.8, B =.8, C = 8. A =.8, B = 8.8, C = 8. Convet the pola equation to a ectangula equation. ) sin θ = 9 = 9 = 9 = 9 + = 9 ) The gaph of a pola equation is given. Select the pola equation fo the gaph. ) ) = 8 cos θ = 8 sin θ = + cos θ = + sin θ ) ) sin θ = = = sin θ = cos θ Test the equation fo smmet with espect to the given ais, line, o pole. ) = cos θ; the pola ais ma o ma not have smmet with espect to pola ais has smmet with espect to pola ais )

5 ) = + sin θ; the line θ = π ) has smmet with espect to the line θ = π ma o ma not have smmet with espect to the line θ = π Use a gaphing utilit to gaph the pola equation. ) = sin θ + cos θ )

6 The gaph of a pola equation is given. Select the pola equation fo the gaph. 7) 7) = sin(θ) = = + cos(θ) = cos(θ)

7 Gaph the pola equation. 8) = + sin θ 8) The ectangula coodinates of a point ae given. Find pola coodinates of the point. 9) (-, - ) (8, ) (, ) (, ) (8, ) 9) Use a pola coodinate sstem to plot the point with the given pola coodinates. 7

8 0) (, - ) 0) Use a gaphing utilit to convet fom ectangula to pola coodinates. Epess the answe in adians. ) (-, -) Round to hundedths and θ to hundedths of adians. (.7, -.) (.7,.) (.7, -.) (.7,.) ) 8

9 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. ) (0, -0) ) 0, - 7π 0, 7π 0, π 0, - 7π Find anothe epesentation, (, θ), fo the point unde the given conditions. ) 9, π, > 0 and -π < θ < 0 ) 9, - π 9, 7 π 9, π 9, - π Solve the tiangle. Round lengths to the neaest tenth and angle measues to the neaest degee. ) a =, c =, B = 07 b = 9.8, A =, C = b =, A =, C = 9 b =.9, A =, C = 7 no tiangle ) ) a =, c =, B = 90 b =., A =.8, C =. b =., A =., C =.8 b =., A =., C =.8 b =., A =.8, C =. ) Use Heonʹs fomula to find the aea of the tiangle. Round to the neaest squae unit. 7) a = 9 inches, b = inches, c = 7 inches 8 squae inches 0 squae inches squae inches 0 squae inches 7) Solve the tiangle. Round lengths to the neaest tenth and angle measues to the neaest degee. 8) 8) 9 A =., B = 0.7, C = 7. A =., B = 7., C = 0.7 A = 7., B =., C = 0.7 A = 7., B = 0.7, C =. Solve the poblem. 9) Two points A and B ae on opposite sides of a building. A suveo selects a thid point C to place a tansit. Point C is feet fom point A and 9 feet fom point B. The angle ACB is. How fa apat ae points A and B? 99. feet 0. feet. feet 7.7 feet 9) 9

10 Solve the tiangle. Round lengths to the neaest tenth and angle measues to the neaest degee. 0) a = 7, b = 7, c = A =., B = 7., C = 7. A = 7., B = 7., C =. A = 7., B =., C = 7. A = 7., B = 7., C =. 0) Solve the poblem. ) Two tacking stations ae on the equato miles apat. A weathe balloon is located on a beaing of N E fom the westen station and on a beaing of N E fom the easten station. How fa is the balloon fom the westen station? Round to the neaest mile. 9 miles 0 miles 0 miles 8 miles ) Find the aea of the tiangle having the given measuements. Round to the neaest squae unit. ) A = 0, b = 7 metes, c = 7 metes 0 squae metes squae metes 0 squae metes 0 squae metes ) Find a. If necessa, ound ou answe to two decimal places. ) ) Two sides and an angle (SS 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 = ) A = 7, C = 9, c = 9 A =, C = 9, c = A = 8, C = 9, c = no tiangle Solve the equation on the inteval [0, π). ) cos + cos + = 0 ) π π π, π π, 7π ) sin + sin = 0 ) π 8, 9π 8 π, π, π, 7π 0, π, π, π no solution Use a calculato to solve the equation on the inteval [0, π). Round the answe to two decimal places. 7) sin = , ,. 0.9,.87.,.99 7) 0

11 Use a half-angle fomula to find the eact value of the epession. 8) sin π 8) Complete the identit. 9) (sin - cos ) =? sin - sin + cos - cos 9) Use the given infomation given to find the eact value of the tigonometic function. 0) cos θ = -, θ lies in quadant III Find cos θ. 0) Use a gaph in a [-π, π, π ] b [-,, ] viewing ectangle to complete the identit. ) - cos sin - =? cos + sin + cos - sin + ) Find the eact value of the epession. ) sin cos + cos sin ) Use tigonometic identities to find the eact value. tan 0 + tan 0 ) - tan 0 tan 0 ) Find the eact value of the epession. ) cos cos - sin sin ) ) cos ( - ) ) Find the eact value b using a sum o diffeence identit. ) sin - ( - ) ( - ) - ( + ) - ( - ) )

12 Wite the epession as the cosine of an angle, knowing that the epession is the ight side of the fomula fo cos ( α - β) with paticula values fo α and β. 7) cos π π cos sin π π sin 7) 9 8 cos ( π ) cos ( π ) cos ( π ) cos ( π ) Complete the identit. 8) sin (α + β) sin (α - β) =? cos β + cos α cos β - cos α sin α - cos β sin β - sin α 8) Find the eact value unde the given conditions. 9) sin α =, 0 < α < π 0 ; cos β = 9, 0 < β < π Find tan (α + β). 9) 7 7 Complete the identit. 0) sin cos + cos sin =? - tan sin tan + cot sec csc 0) ) sin + sin cot =? cot - sin + cot + ) Show that the equation is not an identit b finding a value of fo which both sides ae defined but not equal. ) cos ( - π) = cos ) - π π 0 π Find the eact value of the epession. ) sin- (-0.) ) - π π π 7π ) tan- () ) 7π π π π Use a sketch to find the eact value of the epession. ) csc tan- )

13 Match the function to its gaph. ) = tan ) Gaph the function. 7) = sin ( + π) 7) - - -

14 Detemine the phase shift of the function. 8) = sin (π + ) 8) π units to the ight - π units to the left π units to the left units to the left Detemine the amplitude o peiod as equested. 9) Peiod of = - cos 9) - π π 8π Gaph the function.

15 0) = cos ( - π ) 0) Find the eact value of the indicated tigonometic function of θ. ) tan θ = - 8, θ in quadant II Find cos θ. ) A point on the teminal side of angle θ is given. Find the eact value of the indicated tigonometic function of θ. ) (-, ) Find tan θ. )

16 Find the efeence angle fo the given angle. ) - π ) π π π π 8 A point on the teminal side of angle θ is given. Find the eact value of the indicated tigonometic function of θ. ) (, 0) Find sin θ. ) Find the eact value of the indicated tigonometic function of θ. ) cot θ = - 7, cos θ < 0 Find csc θ. ) Use efeence angles to find the eact value of the epession. Do not use a calculato. ) sin -π ) Find the efeence angle fo the given angle. 7) -7π 7) -π π π 9π 8) π 8) π π π 8 π Find the eact value of the epession if θ =. Do not use a calculato. 9) 7 sin θ ) Use even and odd popeties of the tigonometic functions to find the eact value of the epession. 70) cot - π 70) - undefined 0

17 Sin t and cos t ae given. Use identities to find the indicated value. Whee necessa, ationalize denominatos. 7) sin t = - 7, cos t =. Find tan t. 7) Use even and odd popeties of the tigonometic functions to find the eact value of the epession. 7) cot (- π ) 7) - - Find the eact value. 7) sec π 7) Use a calculato to find the value of the tigonometic function to fou decimal places. 7) tan ) Use even and odd popeties of the tigonometic functions to find the eact value of the epession. 7) sin (- π ) 7) - - 7

18 Answe Ke Testname: TEST # REVIEW MATH FALL 0 ) D ) A ) D ) D ) B ) D 7) A 8) B 9) A 0) C ) B ) C ) D ) B ) A ) B 7) D 8) B 9) D 0) A ) D ) C ) B ) A ) B ) C 7) C 8) C 9) C 0) D ) A ) A ) D ) D ) B ) B 7) D 8) D 9) B 0) C ) B ) A ) C ) B ) B ) B 7) D 8) B 9) C 0) D 8

19 Answe Ke Testname: TEST # REVIEW MATH FALL 0 ) D ) C ) A ) B ) A ) A 7) B 8) C 9) D 0) A ) A ) B ) B ) D ) C ) D 7) B 8) A 9) D 70) C 7) C 7) A 7) B 7) D 7) A 9