Honors PreCalculus Final Exam Review Mr. Serianni

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1 Honors PreCalculus Final Eam Review Mr. Serianni Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the angle to decimal degrees and round to the nearest hundredth of a degree. 1) 95 6''' A) B) 95.0 C) 95.1 D) 95.1 Convert the angle to degrees, minutes, and seconds. ) 19. A) 19 19'1'' B) 19 0'1'' C) 19 19''' D) 19 1''' Convert the degree measurement to radians. Epress answer as multiple of. ) 80 A) B) C) 8 D) 9 Convert the radian measure to degrees. (Round to the nearest hundredth when necessar) ) 18 A) 860 B) 0 C)8 D) 15 Solve the problem. 5) For what numbers θ is f(θ) = cot θ defined? A) all real numbers, ecept odd multiples of (180 ) B) all real numbers, ecept integral multiples of (180 ) C)all real numbers, ecept odd multiples of (90 ) D) all real numbers 6) What is the range of the tangent function? A) all real numbers greater than or equal to 1 or less than or equal to -1 B) all real numbers, ecept odd multiples of (90) C) all real numbers D) all real numbers from -1 to 1, inclusive Use the fact that the trigonometric functions are periodic to find the eact value of the epression. ) tan 1 A) -1 B) C) D) 1 8) tan 90 A) B) - C) D) 1

2 Solve the problem. 9) If sin θ = -0., find the value of sin θ + sin (θ + ) + sin (θ + ). A) -0. B) -0.9 C) D) 1.1 Name the quadrant in which the angle θ lies. 10) csc θ > 0 and sec θ > 0 A) Quadrant III B) Quadrant IV C) Quadrant II D) Quadrant I Use the given values of the sine and cosine to find the function value. 11) sin θ = - A), cos θ =. Find cot θ. B) - C) D) - Find the eact value of the epression. sin 55 1) tan 55 - cos 55 A) 0 B) 1 C) Undefined D) 55 Find the eact value of the requested trigonometric function of θ. 1) csc θ = - and θ in quadrant III Find cot θ. A) - B) - C) D) - 1) sec θ = 9 8 and θ in quadrant IV Find tan θ. A) - 1 B) C) D) Give the amplitude or period as requested. 15) Amplitude of = - sin 5 A) 5 B) C) D) 5 Determine the amplitude and period of the function without graphing. 16) = - sin ( 5 ) A) amplitude = ; period = 5 B) amplitude = ; period = 5 C)amplitude = ; period = 5 D) amplitude = - ; period = 5

3 Find an equation for the graph. 1) A) = cos () B) = cos 1 C) = cos () D) = cos 1 Write the equation of a sine function with the given characteristics. 18) Amplitude = 5 ; Period = 5 A) = 5 sin (10) B) = 5 sin ( 1 10 ) C) = 5 sin ( 5 ) D) = 5 sin ( 5 ) Find the phase shift of the function. 19) = - sin ( - ) A) units up B) / units to the left C)/8 units to the right D) units down 0) = sin ( - 5) A) 5 units to the left B) 5 units to the left C)5 units to the right D) 5 units to the right Solve the problem. 1) The temperature T of a patient during a 5-da illness is given in the following table. Da, Temperature, T Fit a sine function to the data in the table. From the graph of the sinusoidal function of best fit, estimate the highest temperature reached during the 5 -da illness. Round answer to 1 decimal place. A) 105. B) 105. C) 105. D) Graph the function.

4 ) = sec ( 1 ) A) B) C) D)

5 ) = -tan ( + ) A) B) C) D) Find the value of the epression. ) sin A) - 6 B) C) 6 D) 5

6 Find the eact value of each epression. 5) cos-1 (- ) A) 5 6 B) C) - 6 D) 6 Complete the identit. 6) sec - sec tan + tan =? A) 1 B) C)sec + tan D) sec (1 + tan) ) sinθ + tanθ + cosθ =? A) cosθ B) secθ C) tanθ D) sin θ Simplif the epression as far as possible. 8) (1 + cot θ)(1 - cot θ) - csc θ A) B) cot θ C) - cot θ D) 0 Use trigonometric identities to find the eact value. 9) cos 5 1 cos 5 + sin 1 sin A) 1 B) 1 C) D) 1 Find the eact value of the epression. 1 - tan 80 tan 0 0) tan 80 + tan 0 A) - B) C) - D) Find the eact value b using a sum or difference identit. 1) sin 1 A) - ( - 1) B) ( - 1) C) ( - 1) D) - ( - 1) Find the eact value of the epression under the given conditions. ) sin θ = 6 5, tan θ < 0 Find sin (θ). A) 5 B) C) 6 5 D) - 5 6

7 ) sin θ = 0 9, 0 < θ < Find cos (θ). A) B) C) 1 81 D) 81 Using the information given, find the eact value of the trigonometric function. ) Find sin θ, given that tan θ = -, sin θ < 0. A) 5 B) - 5 C) 5 D) - 5 Solve the equation for solutions in the interval 0 θ <. 5) 5 csc θ - = A) B) C) D) Solve the equation. Give a general formula for all the solutions. 6) csc θ = A) θ = + 6k B) θ = 9 + k C)θ = + k D) θ = + 6k 18 Solve the equation for the interval [0, ). ) sin = sin A) = 0,, 6, 5 6 B) =, C) = 6, 5 6 D) =,,, Solve the equation for solutions in the interval 0 θ <. 8) sin = 1 A) No solution B) = 8, 9 8 C) =,, 5, D) = 0,,, Solve the equation on the interval 0 θ <. 9) sin θ = - - cos θ A) B) C) D) 5 Find the missing parts of the triangle. 0) α = 0' β = 10' a = 16.0 A) γ = 11 0', b = 9.5, c = 1.66 B) γ = 111 0', b = 1.66, c = 9.5 C)γ = 11 0', b = 1.66, c = 9.5 D) γ = 111 0', b = 9.5, c = 1.66

8 1) β = 11.6 b = 5.69 a = 9. A) α = 19., γ = 18.9, c = 1.6; B) No solution α' = 160.5, γ' =.8, c' =.8 C)α = 160.5, γ =.8, c =.8 D) α = 19., γ = 18.9, c = 1.6 Solve the problem. ) An airplane is sighted at the same time b two ground observers who are miles apart and in line with the airplane. The report the angles of elevation as 10 and. How high is the airplane? A) 0.6 miles B) 0.5 miles C) 0.5 miles D) 1.5 miles ) Given a triangle with b = 6, c =, and α = 16, what is the length of a? Round the answer to two decimal places. A)a =.9 B)a = C)a =.65 D)a = 1. ) Solve the triangle given that a = 19, b = 16, c = 11. A) α = 5., β = 8.9, γ = 5. B) α = 8.9, β = 5., γ = 5. C)α = 8.9, β = 5., γ = 5. D) α = 5., β = 5., γ = 8.9 5) Two points A and B are on opposite sides of a building. A surveor selects a third point C to place a transit. Point C is 6 feet from point A and 65 feet from point B. The angle ACB is 5. How far apart are points A and B? A) 90. feet B) 6. feet C)5. feet D) 99. feet Find the area of the triangle with the given parts. 6) α =. b = 1.0 in. c =.0 in. A) 1 in. B) 15 in. C) in. D) 1 in. ) a = 11. cm b = 10. cm c = 16.8 cm A) 60 cm B) 6 cm C)5 cm D) 66 cm Find the rectangular coordinates for the point. 8) (9, 10 ) A) - 9, 9 B) 9, -9 C) - 9, -9 D) 9, 9 9) 5, - A) - 5, - 5 B) 5, - 5 C) - 5, 5 D) 5, 5 Find the polar coordinates for the point. 50) (-1,.6) A) (.9, 111 ) B) (-.9, 1.0 ) C)(.9, -1.0 ) D) (.9, 1.0 ) 8

9 Perform the indicated operation. 51)u = -10i - j, v = -i + 8j; Find u + v. A) -1i + j B) -i - 1j C)i + j D) -1i + j Find the magnitude v of the vector. 5)v = 6i + 8j A) 1 B) 100 C) 10 D) 10 Find the unit vector having the same direction as v. 5)v = -5i- 1j A)u = i j B)u = i j C)u = 1 i + 5 j D)u = -65i- 156j 1 Write the vector in the form ai + bj given its magnitude and the angle it makes with the positive -ais. 5) v =, α = 0 A)v = -j B)v = -i C)v = -i - j D)v = ( - ) For the given vectors u and v, find their dot product u v. Round to two decimal places, if necessar. 55)u =.5i + 6.j, v = -.15i +5.60j. A) 5.05 B) 1.6 C) 1.9 D) 0.1 Find the angle between the two vectors. 56)v = -5i + j, w = -6i - j. A) 90 B) C) 0. D) Determine whether the vectors are parallel, orthogonal, or neither. 5)v = i - j, w = i - j A) parallel B) neither C) orthogonal 58)v = i + j, w = i - j A) orthogonal B) parallel C) neither Decompose v into two vectors v1 and v, where v1 is parallel to w and v is orthogonal to w. 59)v = -i + 5j, w = i + j A)v1 = (i + j), v = i j B)v 1 = (i + j), v = 5 i j C)v1 = (i + j), v = i j D)v 1 = - 1 (i + j), v = - 5 i + 1 j Solve the problem. 60) Find the work done b a force of 8 pounds acting in the direction of to the horizontal in moving an object feet from (0, 0) to (, 0). Round answer to the nearest tenth of a foot-pound. A) 0. foot-pounds B) 80.6 foot-pounds C) 8.9 foot-pounds D).5 foot-pounds 9

10 Answer Ke Testname: PC_SEMREVIEW 1) A ) A ) C ) B 5) B 6) C ) D 8) C 9) B 10) D 11) D 1) A 1) C 1) B 15) B 16) A 1) D 18) D 19) C 0) D 1) A ) C ) A ) A 5) A 6) A ) B 8) C 9) C 0) C 1) C ) B ) C ) D 5) C 6) D ) A 8) C 9) D 0) D 1) A ) A ) D ) B 5) C 6) B ) C 8) A 9) C 50) A 10

11 Answer Ke Testname: PC_SEMREVIEW 51) D 5) C 5) B 5) A 55) D 56) B 5) A 58) C 59) C 60) A 11