Eam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Tell in which quadrant or on what coordinate ais the point lies. 1) (, -19) A) Quadrant II B) Quadrant III Quadrant I D) Quadrant IV 1) Find the distance d(p1, P) between the points P1 and P. ) P1 = (6, ); P = (-, -6) A) 18 B) 7 D) 88 ) Solve the problem. ) Find all the points having an -coordinate of 9 whose distance from the point (, -) is 10. A) (9, -1), (9, 8) B) (9, 1), (9, -7) (9, ), (9, -) D) (9, 6), (9, -10) ) List the intercepts of the graph. ) 1 ) -π -π -1 - - - - π π A) - π, 0, (, 0), π, 0 B) 0, - π, (0, ), 0, π - π, 0, (0, ), π, 0 D) 0, - π, (, 0), 0, π List the intercepts for the graph of the equation. ) = + 8 + 16 A) (0, -), (0, -), (16, 0) B) (0, ), (0, ), (16, 0) (-, 0), (-, 0), (0, 16) D) (, 0), (, 0), (0, 16) ) 1
Determine whether the graph of the equation is smmetric with respect to the -ais, the -ais, and/or the origin. 6) = 6) + 9 A) -ais B) -ais origin D) -ais, -ais, origin E) none Solve the problem. 7) Find the equation of a circle in standard form where C(6, -) and D(-, ) are endpoints of a diameter. A) ( + 1) + ( + 1) = B) ( - 1) + ( - 1) = ( + 1) + ( + 1) = 16 D) ( - 1) + ( - 1) = 16 7) Determine whether the relation represents a function. If it is a function, state the domain and range. 8) Alice snake Brad cat Carl dog 8) A) function domain: {Alice, Brad, Carl} range: {snake, cat, dog} B) function domain: {snake, cat, dog} range: {Alice, Brad, Carl} not a function 9) {(-, ), (-1, 0), (0, -1), (1, 0), (, 8)} A) function domain: {, 0, -1, 8} range: {-, -1, 0, 1, } B) function domain: {-, -1, 0, 1, } range: {, 0, -1, 8} not a function 9) Find the value for the function. 10) Find f() when f() = +. A) 6 B) 0 1 D) 10) Find the domain of the function. - 11) h() = - A) { 0} B) { -, 0, } { } D) all real numbers 11) 1) f() = 7 - A) { 7} B) { 7} { 7} D) { 7} 1)
Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if an, and an smmetr with respect to the -ais, the -ais, or the origin. 1) 1) 1 -π -π -π -π π π π π -1 A) function domain: { -π π} range: { -1 1} intercepts: (-π, 0), (- π, 0), (- π, 0), (- π, 0), (0, 0), ( π, 0), ( π, 0), ( π, 0), ( π, 0), (π, 0) smmetr: origin B) function domain: all real numbers range: { -1 1} intercepts: (-π, 0), (- π, 0), (- π, 0), (- π, 0), (0, 0), ( π, 0), ( π, 0), ( π, 0), ( π, 0), (π, 0) smmetr: origin function domain: { -1 1} range: { -π π} intercepts: (-π, 0), (- π, 0), (- π, 0), (- π, 0), (0, 0), ( π, 0), ( π, 0), ( π, 0), ( π, 0), (π, 0) smmetr: none D) not a function Answer the question about the given function. 1) Given the function f() = - 8 + 1, is the point (, ) on the graph of f? A) Yes B) No 1) Determine algebraicall whether the function is even, odd, or neither. 1) f() = + A) even B) odd neither 1)
The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. 16) (-1, 0) 16) 1 - -1 1-1 - - A) increasing B) constant decreasing Use a graphing utilit to graph the function over the indicated interval and approimate an local maima and local minima. Determine where the function is increasing and where it is decreasing. If necessar, round answers to two decimal places. 17) f() = - +, (-1, ) A) local maimum at (, -1) local minimum at (0, ) increasing on (-1, 0) decreasing on (0, ) local maimum at (, -1) local minimum at (0, ) increasing on (-1, 0) and (, ) decreasing on (0, ) B) local maimum at (0, ) local minimum at (, -1) increasing on (-1, 0) and (, ) decreasing on (0, ) D) local maimum at (0, ) local minimum at (, -1) increasing on (0, ) decreasing on (-1, 0) and (, ) 17) Using transformations, sketch the graph of the requested function. 18) The graph of a function f is illustrated. Use the graph of f as the first step toward graphing the function F(), where F() = f( + ) - 1. 18) (-1, 1) - (-, -) - (, -)
A) B) (-, 1) (-, ) - (-, -) (1, -) - - (-, -1) (1, -) - D) (-, 0) (1, 0) - - (-, -) (-1, -) - (1, -) - (, -) Convert the angle to a decimal in degrees. Round the answer to two decimal places. 19) ʹ18ʹʹ A).9 B).9.98 D).88 19) 0) 8 1ʹʹʹ A) 8.18 B) 8. 8. D) 8.8 0) If s denotes the length of the arc of a circle of radius r subtended b a central angle θ, find the missing quantit. 1) r = 1 feet, s = 7 feet, θ =? 1) A) 7 B) 7 radians 1 radians D) 1 Convert the angle in degrees to radians. Epress the answer as multiple of π. ) 7 A) 6π 1 B) π 11 π 1 D) 1π )
Solve the problem. ) The Earth rotates about its pole once ever hours. The distance from the pole to a location on Earth 9 north latitude is about 98 miles. Therefore, a location on Earth at 9 north latitude is spinning on a circle of radius 98 miles. Compute the linear speed on the surface of the Earth at 9 north latitude. A) 680 mph B) 108 mph 68 mph D) 16, mph ) In the problem, t is a real number and P = (, ) is the point on the unit circle that corresponds to t. Find the eact value of the indicated trigonometric function of t. ) ( 8, ) Find tan t. ) 8 A) 8 B) 8 D) Find the eact value. Do not use a calculator. ) sin (- π ) ) A) 1 B) -1 0 D) undefined Find the eact value of the epression if θ =. Do not use a calculator. 6) g(θ) = sin θ Find [g(θ)]. A) 1 B) - D) 6) Find the eact value of the epression. Do not use a calculator. 7) sin π - cos π 6 7) A) 0 B) - 1 D) 1 Find the eact value of the epression if θ = 0. Do not use a calculator. 8) g(θ) = cos θ Find g(θ). A) 1 B) 1 D) 8) Find the eact value of the epression. Do not use a calculator. 9) cos π + tan π 9) A) + 1 B) + 6 1 - D) + A point on the terminal side of an angle θ is given. Find the eact value of the indicated trigonometric function of θ. 0) (-, -1) Find cos θ. 0) A) - B) 1 D) - 1 1 1 1 1 6
Solve the problem. 1) For what numbers θ is f(θ) = tan θ not defined? A) odd multiples of π (90 ) B) all real numbers 1) integral multiples of π (180 ) D) odd multiples of π (180 ) Use the fact that the trigonometric functions are periodic to find the eact value of the epression. Do not use a calculator. ) cot 70 ) A) B) - - D) ) sin 11π ) A) - B) - 1 D) -1 Name the quadrant in which the angle θ lies. ) sin θ > 0, cos θ < 0 A) I B) II III D) IV ) In the problem, sin θ and cos θ are given. Find the eact value of the indicated trigonometric function. ) sin θ = 1, cos θ = 1 Find csc θ. A) B) 1 1 1 D) 1 1 ) Find the eact value of the indicated trigonometric function of θ. 6) cos θ = 8 17, π < θ < π Find cot θ. A) - 1 8 B) - 8 1-8 D) 17 8 6) Use the even-odd properties to find the eact value of the epression. Do not use a calculator. 7) sin (-10 ) A) B) 1-1 D) - 7) Without graphing the function, determine its amplitude or period as requested. 8) = - sin Find the amplitude. A) π B) -π D) π 8) 9) = sin Find the period. 9) A) π B) 1 D) π 7
Answer the question. 0) Which one of the equations below matches the graph? 0) A) = cos B) = cos 1 = - sin D) = sin 1 Find an equation for the graph. 1) 1) 1 -π -π -1 π π - - - - A) = cos 1 B) = cos () = cos () D) = cos 1 Solve the problem. ) For the equation = - 1 period. cos( - π), identif (i) the amplitude, (ii) the phase shift, and (iii) the ) A) (i) 1 (ii) π (iii) π B) (i) (ii) π (iii) π (i) 1 (ii) π (iii) π D) (i) (ii) π (iii) π Find the eact value of the epression. ) cos-1 - ) A) π 6 B) π π 6 D) π 8
) tan-1 ) A) 7π 6 B) π π D) π 6 Find the eact value of the epression. Do not use a calculator. ) sin [sin-1 (0.)] A) B) 0. 0.8 D).0 ) 6) sin-1 sin π 7 6) A) 7 π B) π 7 π 7 D) 7 π Use a calculator to find the value of the epression rounded to two decimal places. 7) sin-1 1 8 7) A) 8.8 B) 7.18 0.1 D) 1. Find the eact solution of the equation. 8) cos-1 = π 8) A) = 0 B) = π = π D) = 1 Find the eact value of the epression. 9) sin (tan-1 ) 9) A) B) D) 0) cos sin-1 0) A) - B) - 1 D) 1) cot-1-1) A) π 6 B) π 6 π D) π ) sec-1 (-) ) A) - π B) π π D) - π Use a calculator to find the value of the epression in radian measure rounded to two decimal places. ) cot-1 A) 1.7 B) 11.1 78.69 D) 0.0 ) 9
Complete the identit. ) (sin θ + cos θ) 1 + sin θ cos θ =? ) A) 1 - sin θ B) -sec θ 1 D) 0 ) cos θ - cos θ sin θ =? A) sec θ B) cos θ tan θ D) sin θ ) Find the eact value of the epression. 6) sin - 11π 1 6) A) - 6 + B) - 6 + 6 D) 6 - Find the eact value under the given conditions. 7) sin α = 1 9, 0 < α < π 1 ; cos β = 1, 0 < β < π Find cos (α + β). 7) A) 77 B) 1 77 1 77 D) 77 8) tan α = 7, π < α < π ; cos β = - 1 1, π < β < π Find sin (α + β). 8) A) B) 0 D) - 6 Find the eact value of the epression. 9) cos tan-1 - sin -1 9) A) B) 6 D) 1 Use the information given about the angle θ, 0 θ π, to find the eact value of the indicated trigonometric function. 60) cos θ = 1 17, π < θ < π Find sin (θ). 60) A) - 161 89 B) 161 89 0 89 D) - 0 89 61) csc θ = -, tan θ > 0 Find cos (θ). 61) A) 1 9 B) - 1 9-9 D) 9 6) cos θ = -, π < θ < π Find cos θ. 6) A) B) - 0 10 D) - 0 10 10
6) sin θ = -, π < θ < π Find sin θ. 6) A) - 0 10 B) - 10 10 D) - Epress the product as a sum containing onl sines or cosines. 6) sin (θ) cos (θ) 6) A) 1 [sin (7θ) + sin (θ)] B) sin cos (10θ ) 1 [sin (7θ) + cos (θ)] D) 1 [cos (7θ) - cos (θ)] Epress the sum or difference as a product of sines and/or cosines. 6) cos (6θ) + cos (θ) A) cos (θ) B) cos (θ) sin θ sin (θ) sin θ D) cos (θ) cos θ 6) Solve the equation on the interval 0 θ < π. 66) sin (θ) = 66) A) π, π B) 0 0, π, π D) π 1, π 6, π, 7π 1, 7π 6, 1π 1, π, 19π 1 Solve the equation. Give a general formula for all the solutions. 67) cos (θ) = 67) A) θ = π 8 + kπ, θ = 7π 8 + kπ B) θ = π 8 + kπ, θ = 7π 8 + kπ θ = π + kπ, θ = π + kπ D) θ = π + kπ, θ = π + kπ Solve the equation on the interval 0 θ < π. 68) sin θ = sin θ 68) A) π 6, π 6 B) π, π, π, π π, π D) 0, π, π 6, π 6 69) sin θ - cos θ = 0 69) A) π, π 6 B) π, π π, π, π, 7π D) π 11
Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give eact answers with rational denominators. 70) Find sin B when b = and c =. 70) A) B) 7 7 7 D) 7 7 Solve the right triangle using the information given. Round answers to two decimal places, if necessar. 71) a =, b = 6; Find c, α, and β. A) c = 7.81 B) c =.7 α = 9.81 α = 9.81 β = 0.19 β = 0.19 c = 7.81 α = 0.81 β = 9.19 D) c =.7 α = 0.81 β = 9.19 71) Solve the triangle. 7) β = 70, γ = 60, b = A) α = 0, c =.69, a =.6 B) α = 0, c =.6, a =.69 α = 0, c =.6, a =.69 D) α = 0, c =.69, a =.6 7) Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve an triangle(s) that results. 7) a = 7, b = 9, β = 9 7) A) one triangle α = 76.01, γ =.99, c = 7.60 B) one triangle α =.9, γ = 9.06, c = 11.88 two triangles α1 = 76.01, γ1 =.99, c1 = 7.60 or α = 10.99, γ = 7.01, c = 1.1 D) no triangle 7) a = 1, b = 8, β = 10 A) two triangles α1 = 1.1, γ1 = 1.9, c1 = 19. or α = 16.9, γ =.1, c =.1 one triangle α = 1.1, γ = 1.9, c = 19. B) one triangle α = 16.9, γ =.1, c =.1 D) no triangle 7) Solve the triangle. 7) b =, c = 6, α = 80 A) a = 8.11, β =.8, γ = 6. B) a = 6.11, β = 6., γ =.8 a = 7.11, β =.8, γ = 6. D) a = 7.11, β = 6., γ =.8 7) 1
Solve the triangle. Find the angles α and β first. 76) a = 7, b = 1, c = 17 A) α = 0., β =.8, γ = 11.9 B) α =., β =.8, γ = 11.9 α =., β =.8, γ = 11.9 D) no triangle 76) Find the area of the triangle. If necessar, round the answer to two decimal places. 77) α = 0, b = 1, c = 6 A) 18 B).18 16 D) 1.18 77) 78) a = 1, b =, c = 6 A) 181.99 B) 80.01 19.69 D) 177.99 78) Match the point in polar coordinates with either A, B, C, or D on the graph. 79) -, π 79) A 1 B - - - - -1 1 r -1 - D C - - - A) A B) B C D) D The polar coordinates of a point are given. Find the rectangular coordinates of the point. 80) 7, π 80) A) - 7, 7 B) 7, -7 7, 7 D) - 7, -7 The rectangular coordinates of a point are given. Find polar coordinates for the point. 81) (-, ) 81) A), - π B) -, - π, π D) -, π Write the comple number in polar form. Epress the argument in degrees, rounded to the nearest tenth, if necessar. 8) - i 8) A) (cos 0 + i sin 0 ) B) (cos 00 + i sin 00 ) (cos 00 + i sin 00 ) D) (cos 0 + i sin 0 ) 1
Solve the problem. Leave our answer in polar form. 8) z = 10(cos + i sin ) w = (cos 1 + i sin 1 ) Find zw. A) (cos 60 + i sin 60 ) B) 0(cos 60 + i sin 60 ) 0(cos 0 + i sin 0 ) D) (cos 0 + i sin 0 ) 8) Write the epression in the standard form a + bi. 8) cos π 6 + i sin π 6 8) A) - 9 + 9 i B) - 9-9 i - 9 + 9 i D) - 9-9 i Find all the comple roots. Leave our answers in polar form with the argument in degrees. 8) The comple fourth roots of -16 8) A) (cos + i sin ), (cos 1 + i sin 1 ), (cos + i sin ), (cos 1 + i sin 1 ) B) (cos 90 + i sin 90 ), (cos 180 + i sin 180 ), (cos 70 + i sin 70 ), (cos 60 + i sin 60 ) 16(cos + i sin ), 16(cos 1 + i sin 1 ), 16(cos + i sin ), 16(cos 1 + i sin 1 ) D) (cos + i sin ), (cos 1 + i sin 1 ), (cos + i sin ), 16(cos 1 + i sin 1 ) The vector v has initial position P and terminal point Q. Write v in the form ai +bj; that is, find its position vector. 86) P = (, ); Q = (-1, -) 86) A) v = 7i + 6j B) v = 6i + 7j v = -6i - 7j D) v = -7i - 6j Solve the problem. 87) If u = -10i - j and v = -i + 7j, find u - v. A) -9i + j B) -10i + j -1i + j D) -8i - 9j 87) 88) If v = 6i - 8j, find v. A) 1 B) 100 10 D) 10 88) Write the vector v in the form ai + bj, given its magnitude v and the angle α it makes with the positive -ais. 89) v = 1, α = 10 89) A) v = 1-1 i - 1 j B) v = 1-1 i - 1 j v = 1 - i - 1 j D) v = 1 i - 1 j 1
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 90) An audio speaker that weighs 0 pounds hangs from the ceiling of a restaurant from two cables as shown in the figure. To two decimal places, what is the tension in the two cables? 90) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the dot product v w. 91) v = 1i + j, w = -1i - j A) -18 B) -1-160 D) -16 91) Find the angle between v and w. Round our answer to one decimal place, if necessar. 9) v = -i + 7j, w = -6i - j A) 90.9 B) 88. 110.8 D) 0.7 9) Solve the problem. 9) Which of the following vectors is parallel to v = -10i - 8j? A) w = 0i + 16j B) w = i - j w = -0i + j D) w = i + j 9) State whether the vectors are parallel, orthogonal, or neither. 9) v = i + j, w = 6i + 8j A) Parallel B) Orthogonal Neither 9) 9) v = i + j, w = i - j A) Orthogonal B) Parallel Neither 9) Solve the problem. Round our answer to the nearest tenth. 96) A wagon is pulled horizontall b eerting a force of 60 pounds on the handle at an angle of to the horizontal. How much work is done in moving the wagon 0 feet? ʺ. A) 718.9 ft-lb B) 110.8 ft-lb 1617. ft-lb D) 167.9 ft-lb 96) 1
Answer Ke Testname: TRIG FINAL 1) D ) A ) D ) C ) C 6) C 7) B 8) C 9) B 10) A 11) B 1) C 1) A 1) B 1) B 16) C 17) B 18) C 19) B 0) B 1) C ) C ) A ) C ) B 6) A 7) A 8) B 9) C 0) A 1) A ) D ) A ) B ) A 6) B 7) D 8) B 9) D 0) B 1) D ) A ) C ) D ) B 6) C 7) C 8) A 9) B 0) D 16
Answer Ke Testname: TRIG FINAL 1) B ) C ) D ) C ) B 6) B 7) C 8) D 9) C 60) D 61) A 6) B 6) B 6) A 6) D 66) D 67) B 68) D 69) C 70) A 71) A 7) A 7) B 7) A 7) C 76) B 77) A 78) D 79) D 80) A 81) C 8) D 8) B 8) B 8) D 86) C 87) D 88) C 89) B 90) Tension in right cable:.90 lb; tension in left cable: 1.9 lb 91) C 9) B 9) A 9) A 9) A 96) A 17