SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 4) cot! sec! sin! 4) 6) sin! cos! sec! csc!

Transcription

1 Sem 1 Final Eam Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use basic identities to simplif the epression. 1) tan! sec! 1) 2) tan 2! csc 2! 2) 3) csc! cot! sec! 3) 4) cot! sec! sin! 4) 5) 1 cot 2! + sec! cos! 5) 6) sin! cos! sec! csc! 6) 7) cos! - cos! sin 2! 7) 8) tan! cot! 8) Find all solutions in the interval [0, 2!). 9) cos cos + 1 = 0 9) ) 2 sin 2 = sin ) 11) cos = sin 11) 12) sec 2-2 = tan 2 12) 1

2 Find the trigonometric function value for the angle shown. 13) sin! 13) 14) tan! 14) 15) cos! 15) 2

3 16) cot! 16) Find the range of the function. 17) f() = ) 18) f() = ) 19) f() = ) 20) f() = ) 21) = ) 22) f() = ) Determine algebraicall whether the function is even, odd, or neither even nor odd. 23) f() = ) 24) f() = ) 25) f() = ) 26) f() = ) 27) f() = -1 27) 28) f() = ) 3

4 Find the asmptote(s) of the given function. 29) f() = vertical asmptotes(s) 29) 30) h() = ( - 1)( + 5) 2-4 vertical asmptotes(s) 30) 31) f() = vertical asmptotes(s) 31) 32) f() = vertical asmptotes(s) 32) 33) g() = - 5 vertical asmptotes(s) 33) ( - 9)( + 8) 34) f() = horizontal asmptotes(s) 34) 35) g() = horizontal asmptotes(s) 35) 36) g() = horizontal asmptotes(s) 36) Suppose that! is in standard position and the given point is on the terminal side of!. Give the eact value of the indicated trig function for!. 37) (9, 12); find sin!. 37) 38) (6, 8); find cos!. 38) 39) (-20, 48); find sin!. 39) 40) (15, 20); find csc!. 40) Determine whether the equation defines as a function of. 41) = 8 41) 42) = ) 43) 2 = ( - 9)( + 5) 43) 4

5 44) = 5 44) Solve the problem. 45) Sue invested $,000, part at 5.1% annual interest and the balance at 6.3% annual interest. How much is invested at each rate if a 1-ear interest pament is $582.72? 45) 46) Helen Weller invested $,000 in an account that pas % simple interest. How much additional mone must be invested in an account that pas 13% simple interest so that the average return on the two investments amounts to 11%? 46) Use an equation to solve the problem. 47) If Gloria received a 3% raise and is now making $21,630 a ear, what was her salar before the raise? 47) 48) On Monda, an investor bought 0 shares of stock. On Tuesda, the value of the shares went up 5%. How much did the investor pa for the 0 shares if he sold them Wednesda morning for $ ? 48) Write the specified quantit as a function of the specified variable. 49) A square is inscribed in a circle. Write the area of the square as a function of the radius. 49) 50) The base of an isosceles triangle is a fourth as long as the two equal sides. Write the area of the triangle as a function of the length of the base. 50) Solve the problem. 51) A contractor needs to know the height of a building to estimate the cost of a job. From a point 88 feet awa from the base of the building, the angle of elevation to the top of the building is found to be Find the height of the building. Round our answer to the hundredths place. 51) 52) On a sunn da, a flag pole and its shadow form the sides of a right triangle. If the hpotenuse is 50 m long and the shadow is 40 m, how tall is the flag pole? 52) 53) Suppose that the average monthl low temperatures for a small town are shown in the table. Month Temperature ( F) ) Model this data using f = a sin b - c + d. 54) The number of hours of darkness in a coastal town can be modeled b f() = 6.1 cos " , where is the month and = 1 corresponds to Januar. 54) Approimate the number of hours of darkness in April, to the nearest tenth of an hour. 5

6 55) A contractor needs to know the height of a building to estimate the cost of a job. From a point 99 feet awa from the base of the building, the angle of elevation to the top of the building is found to be Find the height of the building. Round our answer to the hundredths place. 55) 56) A contractor needs to know the height of a building to estimate the cost of a job. From a point 90 feet awa from the base of the building, the angle of elevation to the top of the building is found to be Find the height of the building. Round our answer to the hundredths place. 56) 57) On a sunn da, a flag pole and its shadow form the sides of a right triangle. If the hpotenuse is 35 m long and the shadow is 28 m, how tall is the flag pole? 57) Solve the equation. 58) 55b + 35 = 15b 58) 59) 32( - 128) = 64 59) 60) ( - 11) - ( + ) = 4 60) Solve the inequalit and draw a number line graph of the solution. 61) < ) ) + 2 > 3 62) ) 4-3 > ) Find a general form equation for the line through the pair of points. 64) (3, 5) and (-7, 2) 64) 65) (-2, 4) and (5, 1) 65) 66) (-3, -4) and (8, -2) 66) 6

7 Graph the piecewise-defined function. if < 0 67) f() = cos if 0 67) ) h() = 3 if < 0 if 0 68) Find the domain of the given function. 69) f() = 14-69) 70) f() = ) 71) f() = ( + 2)( - 2) ) 72) f() = + 9 ( + 4)( - 8) 72) 73) f = -6 73) 7

8 74) f = ) 75) f() = ) 76) f() = ) 77) f() = ) 78) f() = ) Write the epression as the sine, cosine, or tangent of an angle. 79) sin " 5 cos " 11 + cos " 5 sin " 11 79) 80) cos " 5 cos " 7 + sin " 5 sin " 7 80) 81) cos " 6 cos - sin " 6 sin 81) 82) sin 8 cos - cos 8 sin 82) 83) cos 7 cos 2 - sin 7 sin 2 83) 84) tan 59 - tan tan 59 tan 11 84) 85) tan ("/11) + tan ("/5) 1 - tan ("/11) tan ("/5) 85) Solve the problem. 86) A pendulum of length L, when displaced horizontall and released, oscillates with harmonic motion according to the equation = A sin(( g/l)t + "/2), where is the distance in meters from the rest position t seconds after release, and g = 9.8 m/s 2. Identif the period, amplitude, and phase shift when A = 0. m and L = 1.96 m. 86) 8

9 87) Use the graph of f to estimate the local maimum and local minimum. 87) Solve the equation algebraicall. 88) = 0 88) 89) = 0 89) Give the equation of the function g whose graph is described. 90) The graph of f() = is verticall stretched b a factor of 3.9. This graph is then reflected across the -ais. Finall, the graph is shifted 0.6 units downward. 90) Find all solutions to the equation. 91) 4 sin 2-4 sin + 1 = 0 91) 92) cos cos + 1 = 0 92) Find all solutions in the interval [0, 2!). 93) sec 2-2 = tan 2 93) 94) tan 2 = 1 + cos 1 - cos 94) 95) sin 2 - cos 2 = 0 95) 96) cot 2 = 1 - cos 1 + cos 96) 97) 2 sin 2 = sin 97) 9

10 Graph the function and determine if it has a point of discontinuit at = 0. If there is a discontinuit, tell whether it is removable or non-removable. 98) h() = 98) Determine whether the graph is the graph of a function. 99) 99) ) 0) Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. 1) 7" 9 1)

11 2) ) The graph is that of a function = f() that can be obtained b transforming the graph of = the function f. 3). Write a formula for 3) Find the eact solution to the equation without a calculator. 4) sin -1 (sin ) = " 4 4) 5) 6 arcsin = " 5) Find the inverse of the function. 6) f() = ) Solve. 7) To find the distance AB across a river, a distance BC of 146 m is laid off on one side of the river. It is found that B = 2.4 and C = Find AB. 7) 8) Points A and B are on opposite sides of a lake. A point C is 88.6 meters from A. The measure of angle BAC is 80 40', and the measure of angle ACB is determined to be 40 30'. Find the distance between points A and B (to the nearest meter). 8) Perform the requested operation or operations. 9) f() = + 4; g() = 8-8, find f(g()). 9) 1) f() = 6 + 8; g() = 3-1, find f(g()). 1) Find the eact value b using a half-angle identit. 111) tan ) 112) cos - " 8 112) 11

12 113) sin ) Use the fundamental identities to find the value of the trigonometric function. 114) Find cos! if sin! = - 12 and tan! > ) ) Find cot! if csc! = 37 6 and tan! > ) 116) Find cot! if csc! = 3 and tan! > ) Find the zeros of the function in the interval [-2!, 2!]. 117) f() = sin 2 117) 118) f() = 3 cos 118) Use the arc length formula and the given information to find the indicated quantit. 119) s = 6.4 ft,! = " 5 rad; find r 119) 120) s = 19 m, r = 6 m; find! 120) Describe the transformations required to obtain the graph of the function f() from the graph of the function g(). 121) f() = sin (-7) ; g() = sin 121) 122) f() = cos 6 ; g() = cos 122) Determine if the function is one-to-one. 123) 123)

13 Simplif the epression. 124) csc " - cos (-) 124) 2 125) sin2-1 cos (-) 125) 126) 1 csc - cot + 1 csc + cot 126) 127) cos " 2 - tan sin 2 127) Determine the intervals on which the function is increasing, decreasing, and constant. 128) 128) - 129) 129) - - Evaluate the trigonometric function of the given quadrantal angle. 130) sin ) 131) cos 3" 131) 13

14 Evaluate without using a calculator b using ratios in a reference triangle. 132) cos (- 5" 4 ) 132) 133) tan (- 2" 3 ) 133) Determine if the function is bounded above, bounded below, bounded on its domain, or unbounded on its domain. 134) = ) 135) = 0 135) Find the area. Round our answer to the nearest hundredth if necessar. 136) Find the area of the triangle with the following measurements: B = 68, a = 14 cm, c = 20 cm 136) 137) Find the area of the triangle with the following measurements: C = 8, a = 1.7 in., b = 4.9 in. 137) 138) Find the area of the triangle with the following measurements: C = 84, a = 2.9 in., b = 6.4 in. 138) State whether the given measurements determine zero, one, or two triangles. 139) A = 43, a = 3, b = ) 140) A = 77, a = 26, b = ) 141) B = 85, b = 24, c = ) 142) B = 78, b = 25, c = ) 143) C = 44, a = 22, c = ) 144) C = 31, a = 32, c = ) Provide an appropriate response. 145) Under which of the following conditions do we know that two triangles are congruent? (More than one ma appl.) 145) (i) Three sides of one triangle are equal to the corresponding sides of the second triangle. (ii) Three angles of one triangle are equal to the corresponding angles of the second triangle. (iii) Two angles and the included side of one triangle are equal to the corresponding parts of the second triangle. 14