Precalculus A - Final Exam Review Fall, 2014

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1 Name: Precalculus A - Final Exam Review Fall, 2014 Period: Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. 1) 85 2) ) 3 Convert the radian measure to degree measure. Use the value of found on a calculator and round answers to two decimal places. 15) 4 Draw the angle having the radian measure. 16) Find the angle of smallest possible positive measure that is coterminal with the given angle. 4) ) 403 6) ) 225 Convert the angle to decimal degrees and round to the nearest hundredth of a degree. 7) 15 8'25'' 8) 191 3'52'' Convert the angle to degrees, minutes, and seconds. 9) ) Convert the angle to radians. Leave as a multiple of. 11) ) 1080 Convert the radian measure to degree measure. 13) Find the reference angle for the given angle. 18) 23 19) ) 432 Use a calculator to find the function value to four decimal places. 21) sin (696 ) 22) cos(13/24) 23) sin (27 15') Convert the degree measure to radian measure. Use the value of found on a calculator and round answers to three decimal places. 14) Solve the problem. 24) Find sin (), given that cos () = 2 9 quadrant IV. and in 1

2 25) Find cos (), given that sin () = 4 and cos () 7 < 0 Find the exact value of the indicated trigonometric function of, if is an angle in standard position whose terminal side contains the given point. 26) (12, 16); Find sin. The figure shows angle in standard position with its terminal side intersecting the unit circle. Evaluate sin and cos. 34) , ) (-4, 9); Find tan. 28) (9, 12); Find cos. Evaluate the function requested. Write your answer as a fraction in lowest terms. 29) Find tan A. 48 Solve the right triangle with the given sides and angles. 35) a = 3.5, = 42.4 Find the value of s in the interval [0, /2] that makes the statement true. 30) sin s = ) csc s = Solve the triangle with the given parts. 36) 20 32) cot s = ) sec s = Solve the triangle. If there is more than one triangle with the given parts, give both solutions. 37) = 99.6 b = 6.64 a = ) = b = a = Find the area of triangle ABC. 39) = 28.8 b = 12.7 c = 7.4 2

3 Solve the problem. 40) A triangular-shaped field has sides of m and m, and the angle between them measures Find the area of the field. Solve the triangle with the given information. 41) = b = 4.70 a = ) A fire is sighted due west of lookout A. The bearing of the fire from lookout B, 5.2 miles due south of A, is N 39 12'W. How far is the fire from B (to the nearest tenth of a mile)? Graph the function. 48) y = sin 2x 42) a = 6.7 b = 13.2 c = 16.9 Solve the problem. 43) To find the distance AB across a river, a distance BC = 211 m is laid off on one side of the river. It is found that = and = Find AB. 44) To find the distance between two small towns, an electronic distance measuring (EDM) instrument is placed on a hill from which both towns are visible. If the distance from the EDM to the towns is 4.2 miles and 4.9 miles and the angle between the two lines of sight is 37, what is the distance between the towns? Round your answer to the nearest tenth of a mile. 49) y = -cos x 45) A 39-foot ladder is leaning against the side of a building. If the ladder makes an angle of 26 4 with the side of the building, how far up from the ground does the ladder make contact with the building? Round your answer to the hundredths place. 46) Find h as indicated in the figure. Round your answer to the hundredths place. Solve the problem. 50) Suppose that the average monthly low temperatures for a small town are shown in the table. Month Temperature ( F) Model this data using f(x) = A sin[b(x - C)] + D ft 3

4 Graph the function. 51) y = sec x - 4 Find the phase shift of the function. 62) y = 2 cos x + 4 Solve the equation for solutions in the interval [0, 2). 63) 2 sin 2 x - 4 sin x + 8 = 6 Solve the equation for all values 0 x ) sin 4x = 2 65) 2 cos 2x = 1 Find the amplitude or period as requested. Solve the equation for solutions in the interval [0, 360 ). 66) tan 4 = 0 52) Find the period of y = -3 sin 8x ) sin 2 = ) Find the amplitude of y = -2 sin 3x + 4. Find the phase shift of the function. 54) y = 5 sin 4x - 2 Evaluate the expression. Provide an appropriate response. 68) Explain what is wrong with the following solution for the equation tan 2 = 2 in the interval [0, 2). tan 2 = 2 tan = 1 = 4 or = ) cos arcsin ) sin (arctan 2) Write the following as an algebraic expression in u, u > 0. 57) cos(arctan u) 58) sin arctan u 3 Solve the equation for solutions in the interval [0, 2). 59) 8 sin x + 7 = 11 60) 4 tan x + 7 = 11 Write an equation for a sine curve that has the given amplitude, period, and phase shift. 61) 6, 2, 8 4

5 Answer Key Testname: FINAL EXAM REVIEW PRECAL FALL ) 445 ; ) 194 ; ) 7 3 ; ) 196 5) 43 6) 4 3 7) ) ) 59 52'48'' 10) '24'' 11) ) 6 13) ) ) ) 17) 18) 23 19) 68 20) 72 21) ) ) ) )

6 Answer Key Testname: FINAL EXAM REVIEW PRECAL FALL ) ) ) ) tan A = ) ) ) ) ) sin = 12 13, cos = ) = 47.6, b = 3.2, c = ) = 103, a = 9, b = 16 37) No solution 38) = 30.00, = , c = 42.40; ' = , ' = 10.11, c' = ) ) 20,039 m2 41) c = 15.2, = 43.8, = ) = 21.6, = 46.4, = ) 65 m 44) 3.0 miles 45) ft 46) ft 47) 6.7 mi 48) 6

7 Answer Key Testname: FINAL EXAM REVIEW PRECAL FALL ) 50) f(x) = 23 sin (x - 4) ) 52) 4 53) 2 54) 8 55) ) ) u2 + 1 u ) u u u ) 60) 6, 5 6 4, 5 4 7

8 Answer Key Testname: FINAL EXAM REVIEW PRECAL FALL ) y = 6 sin 1 x ) ) 64) 65) 2 12, 6, 2 3, 7 12, 7 6, 13 12, 5 3, , 9 8, 7 8, ) {0, 45, 90, 135, 180, 225, 270, 315 } 67) {105, 165, 285, 345 } 68) Answers will vary. tan 2 2 tan, so the first equation cannot be divided by 2. 8

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