Solution Manual for Trigonometry 2nd Edition by Stewart NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Trigonometry, 2e Trig Chapter Fundamentals 1.1 Coordinate Geometry The point that is units to the right of the y -axis and units below the x -axis has coordinates a, b The distance between the points 1,2 and 7,10 is The point midway between and 7,10 If the point a, b and c, d c a is 10 c, d and 3, 5 d b So the distance between 62 82 36 64 100 10 a c b d ¬ is , So the point midway between đ 2 đ 2 ưđ 1,2 10 12 is , , 4, 2, is on the graph of an equation in x and y , then the equation is satisfied when we replace ? ? x by and y by We check whether This is false, so the point 2, is not on the graph of the equation 2y x (a) To find the x -intercept(s) of the graph of an equation we set y equal to in the equation and solve for x : x x 1 , so the x -intercept of 2y x is 1 (b) To find the y -intercept(s) of the graph of an equation we set x equal to in the equation and solve for y : 2y y The graph of the equation , so the y -intercept of 2y x is 2 x y is a circle with center 1,2 and radius 9 3 Z @ @ M Y @@ @ A 5,1 , B 1,2 , C 2, , D 6,2 , E 4, 1 , F 2, , G 1, 3 , H 2, 2 The two points are (a) d 0,2 3, and 2 0 ¬ (b) midpoint: , 2 ® 32 22 9 4 13 23 , INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Solution Manual for Trigonometry 2nd Edition by Stewart NOT FOR SALE Full file 2at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Chapter 1: Functions nctions and Graphs Gra 2, 1 10 The two points are (a) d 2 and 2,2 2 1 ưđ 4 2 1 (b) midpoint: , 0, 3, 11 The two points are (a) d 2 3 2 3 16 25 5, 3 and 3 8 62 64 36 100 10 3 3 ¬ 1, (b) midpoint: , 2, 3 12 The two points are (a) d ® 2 and 4, 1 2 3 1 6 2 36 50 10 2 3 1 ¬ 1, 2 (b) midpoint: , ® 13 (a) 14 (a) Z Z @ M Y M Y (b) d (b) 6 16 8 100 10 16 ¬ (c) midpoint: , 3,12 2 ® d 2 10 12 5 5 169 13 2 10 ¬ (c) midpoint: , 4, 2 ® INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Solution Manual for Trigonometry 2nd Edition by Stewart NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Trigonometry, 2e Trig 15 (a) 16 (a) Z Z M M @@ Y @@ (b) Y (b) 3 d 7 625 25 6 18 d 24 49 576 ưđ 3 6 18 (c) midpoint: , , 2 2 1 10 200 10 2 1 10 ¬ ® 1 (c) midpoint: , 4, 2 18 (a) 17 (a) Z Z @ M M @ Y Y @ (b) (b) d 6 2 2 122 4 144 16 160 10 2 ¬ (c) midpoint: , 0, 2 ® d 6 52 6 25 36 61 6 ¬ (c) midpoint: , , 3 2 ® INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Solution Manual for Trigonometry 2nd Edition by Stewart NOT FOR SALE Full file 4at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Chapter 1: Functions nctions and Graphs Gra 19 d A, B d A,C 2 3 4 3 4 So the area is ¸ 24 Z # $ M Y % & 20 The area of a parallelogram is its base times its height Since two sides are parallel to the x -axis, we use the length of one of these as the base Thus, the base is d A, B (1 5)2 (2 2)2 (4)2 The height is the change in the y coordinates, thus, the height is So the area of the parallelogram is base ¸ height ¸ 16 Z M % & # $ Y 21 From the graph, the quadrilateral ABCD has a pair of parallel sides, so ABCD is a trapezoid The area is b1 b2 ¬ h From the graph we see that b1 d A, B ® b2 d C , D 2 3 0 42 ; 22 ; and h is the difference in y -coordinates is ¬ Thus the area of the trapezoid is 3 ® Z & M # % $ Y INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Solution Manual for Trigonometry 2nd Edition by Stewart NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Trigonometry, 2e Trig 22 The point S must be located at 0, 4 To find the area, we find the length of one side and square it This gives d Q, R So the area is Z 50 5 2 1 5 5 25 25 50 50 M Y 23 24 Z Z M Y 25 Y 26 Z Z M M Y Y INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Solution Manual for Trigonometry 2nd Edition by Stewart NOT FOR SALE Full file 6at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Chapter 1: Functions nctions and Graphs Gra 28 27 Z Z 29 Y Y Y 30 Z Z M Y 31 32 Z Z M 33 d 0, A d 0, B Thus point Y 7 62 72 2 5 5 A 6, is closer to the origin 34 d E ,C Y 6 2 d E , D 2 Thus point C is closer to point E 36 49 82 4 25 64 22 52 1 85 89 16 25 20 26 INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Solution Manual for Trigonometry 2nd Edition by Stewart NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Trigonometry, 2e Trig 35 d P, R d Q, R is closer to point R 7, 3 7 1 1 36 (a) The distance from 1 4 1 2 4 16 20 16 Thus point Q 1, to the origin is 72 32 49 58 The distance from 3, to the origin is 32 72 49 58 So the points are the same distance from the origin (b) The distance from b, a to the origin is a, b to the origin is b a b a b a a b The distance from a b So the points are the same distance from the origin 37 Since we not know which pair are isosceles, we find the length of all three sides 2 d A, B 3 d C , B 3 1 3 1 2 9 9 16 3 12 4 18 17 d A,C 4 42 1 16 17 So sides AC and CB have the same length 38 Since the side AB is parallel to the x -axis, we use this as the base in the formula area 21 base ¸ height The height is the change in the y -coordinates Thus, the base is 2 6 ¸ 3, 1 , and C 3, 3 So So the area is and the height is A 2,2 , B 39 (a) Here we have 2 d A, B 1 d C , B 3 d A,C 3 2 2 12 3 1 3 3 2 1 9 62 22 5 5 10 ; 36 25 25 40 10 ; 50 Since d A, B ¯ d C , B ¯ d A,C ¯ , we conclude that the triangle is a right triangle ¢ ± ¢ ± ¢ ± (b) The area of the triangle is ¸ d C , B ¸ d A, B 21 ¸ 10 ¸ 10 10 INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Solution Manual for Trigonometry 2nd Edition by Stewart NOT FOR SALE Full file 8at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Chapter 1: Functions nctions and Graphs Gra 40 d A, B 11 3 7 d A,C d B,C 11 2 52 42 4 2 52 2 3 25 16 9 12 41 ; 16 25 41 ; 81 82 Since d A, B ¯ d A,C ¯ d B,C ¯ , we conclude that the triangle is a right triangle The area ± ¢ ± ¢ ± ¢ is 41 ¸ 41 41 41 We show that all sides are the same length (its a rhombus) and then show that the diagonals are equal Here we have A 2, , B 4, , C 1, , and D 5, So 2 d A, B 2 d B,C d C , D 5 d D, A 2 5 6 2 0 3 2 36 45 ; 36 45 ; 6 3 62 3 6 9 3 32 62 36 36 45 ; 45 So the points form a rhombus Also d A,C 2 and d B,D 0 5 32 9 2 3 9 81 3 90 10 , 81 90 10 Since the diagonals are equal, the rhombus is a square 42 d A, B d B, C 2 1 11 15 11 d A,C 42 82 22 42 16 64 16 20 1 15 62 122 36 144 d A, B d B,C d A,C , and the points are collinear 43 Let P 0, y be such a point Setting the distances equal we get y 5 y 80 180 So y 2y º y 10y 50 y 2y 25 y 10y 25 12y 48 y 4 Thus, the point is P 0, 4 Check: 4 5 4 2 5 1 12 25 26 ; 25 26 5 INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Solution Manual for Trigonometry 2nd Edition by Stewart NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Trigonometry, 2e Trig ¬ 44 The midpoint of AB is C a , 2, So the length of the median 2 d C ,C a 2 3 ® CC a is 37 The midpoint of AC is ¬ B a , 29 ,1 So the length of the median BB a is d B, B a 2 ® 29 ¬ 109 The midpoint of BC is Aa , , So 11 2 ® 2 1 the length of the median 45 As indicated by Example 3, we must find a point 145 such that the midpoints of PR and of QS 112 AAa is d A, Aa S x1, y1 4 1 4 ¬ x y ¬ Setting the x -coordinates equal, we are the same Thus , , 1 2 ® 2 ® x1 x 1 x1 Setting the y -coordinates equal, we 2 4 y1 y1 y1 3 Thus S 2, 3 get 2 get Z M Y 2 x 2 x to find the x coordinate of B This gives 2 3 y x 10 Likewise, 16 y y 13 Thus, 46 We solve the equation 12 x B 10,13 INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Solution Manual for Trigonometry 2nd Edition by Stewart NOT FOR SALE Full file 10 at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Chapter 1: Functions unctions and Graphs Gr 47 (a) Z % & $ M # Y ¬ ® 2 1 , (b) The midpoint of AC is , , the midpoint of BD is 2 4 ¬ , 25 , ® (c) Since the they have the same midpoint, we conclude that the diagonals bisect each other a b ¬ 48 We have M , 2 ưđ a b ơư , Thus, 2 ® d C , M a ¬2 ¬2 b ® ® a b2 4 d A, M ¬2 ¬2 a a b ® ® a ¬2 b ¬2 ® ® a b2 4 a b2 ; d B, M a ¬2 ¬2 b b ® ® a ¬2 b ¬2 ® ® a b2 4 a b2 49 0, : 1, : a b2 ; ? ? 1 No ? ? 1 Yes ? ? 1, 1 : 1 1 1 Yes So 1, and 1, 1 are points on the graph of this equation ? 50 ? 1,1 : ¡ ¯° No ¢ ± : 1, 21 ? ? 2 ¡¢ ¯°± ? 2 Yes ? : ¡¢ 1 ¯°± 21 1 Yes So both 1, and 1, are points on the graph of this equation 2 1, 21 INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Solution Manual for Trigonometry 2nd Edition by Stewart NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Trigonometry, T Trigo rigo 2e 11 51 2 ? ? 0, 2 : 2 2 0 Yes 1, 2 : ? ? 2 2 No 2 ? ? 2, 2 : 2 2 4 Yes So 0, 2 and 2, 2 are points on the graph of this equation 52 0,1 : , 2 3,1 2 ? ? Yes : 2 2 2 2 1 21 Yes ? ? So 0,1 , , , and , 2 2 : ? ? 14 Yes are all points on the graph of this equation 4x x x x x or x , so the x -intercept are and To find y -intercepts, set x This gives 53 To find x -intercepts, set y This gives y 02 y , so the y -intercept is 54 To find x -intercepts, set y This gives x 02 x2 1 x2 9 x o3 , so the x -intercept are 3 and 02 y y2 To find y -intercepts, set x This gives 1 y2 4 x o2 , so the y -intercept are 2 and 55 To find x -intercepts, set y This gives x 02 x 16 x 16 x o2 So the x -intercept are 2 and To find y -intercepts, set x This gives 04 y y 16 y 16 y o4 So the y -intercept are 4 and 56 To find x -intercepts, set y This gives x 03 x 64 x 64 x o8 So the x -intercept are 8 and To find y -intercepts, set x This gives 02 y y 64 y 64 y So the y -intercept is INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Solution Manual for Trigonometry 2nd Edition by Stewart NOT FOR SALE Full file 12 at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Chapter 1: Functions unctions and Graphs Gr 57 y x y x 4 2 2 When y we get x So the x intercept is , and x 58 y 3x y x 3 6 2 3 1 0 12 º y , so the y -intercept is x -axis symmetry: y x y x , which is not the same as y x , so the graph is not symmetric with respect to the x -axis y -axis symmetry: y x y x , which is not the same as y x , so the graph is not symmetric with respect to the y -axis Origin symmetry: y x y x , which is not the same as y x , so the graph is not symmetric with respect to the origin Z y º 3x 3x 3 x 1 , so the x -intercept is 1 , and x º y , so the y intercept is x -axis symmetry: y 3x y 3x , which is not the same as y 3x , so the graph is not symmetric with respect to the x -axis y -axis symmetry: y x y 3x , which is not the same as y 3x , so the graph is not symmetric with respect to the y -axis Origin symmetry: y x y 3x , which is not the same as y 3x , so the graph is not symmetric with respect to the origin Z M Y M Y INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Solution Manual for Trigonometry 2nd Edition by Stewart NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Trigonometry, T Trigo rigo 2e 13 59 2x y y x 1 8 6 4 2 When y we get 2x So the x - 60 Solve for y : x y y x y x 2 1 2 1 y º x x , so intercept is When x we get y the x -intercept is , and x so the y -intercept is 6 x -axis symmetry: 2x y 2x y , which is not the same, so the graph is not symmetric with respect to the x -axis y -axis symmetry: x y 2x y 6 , so the graph is not symmetric with respect to the y -axis Origin symmetry: x y 2x y , which not he same, so the graph is not symmetric with respect to the origin º y , so the y -intercept is x -axis symmetry: x y x y , which is not the same as x y , so the graph is not symmetric with respect to the x -axis y -axis symmetry: x y x y , which is not the same as x y , so the graph is not symmetric with respect to the y -axis Origin symmetry: x y x y , which is not the same as x y , so the graph is not symmetric with Z respect to the origin Z M Y M Y INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Solution Manual for Trigonometry 2nd Edition by Stewart NOT FOR SALE Full file 14 at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Chapter 1: Functions unctions and Graphs Gr 61 y x2 x 3 2 1 62 y 8 3 3 8 y x2 x 3 2 1 y º x2 x2 º x o1 , so the x -intercepts are and 1 , º y , so the y -intercept is and x x -axis symmetry: y x y x ,which is not the same as y x , so the graph is not symmetric with respect to the x -axis y -axis symmetry: y x y x , so the graph is symmetric with respect to the y -axis Origin symmetry: y x y x which is not the same as y x The graph is not symmetric with respect to the origin y 11 3 11 y º x 2 2 x , since x p , there is no x -intercept, and x º y , so the y intercept is x -axis symmetry: y x 2 y x 2 , which is not the same, so the graph is not symmetric with respect to the x -axis y -axis symmetry: y x x 2 , so the graph is symmetric with respect to the y axis Origin symmetry: y x 2 y x 2 , which is not the same, so the graph is not symmetric with respect to the origin Z Z M Y M Y INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Solution Manual for Trigonometry 2nd Edition by Stewart NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Trigonometry, T Trigo rigo 2e 15 63 4y x y 14 x 64 y 1 x 6 4 2 4 y 27 8 1 27 x 6 4 2 y º 14 x x º x , so the x -intercept is , and x º y 8y x y 18 x , so the y -intercept is x -axis symmetry: y 14 x , which is not the y 14 x , so the graph is not symmetric with respect to the x -axis same as y -axis symmetry: y x y 14 x , so the graph is symmetric with respect to the y -axis Origin symmetry: y 14 x y º 18 x x º x , so the x -intercept is , and x º y , so the y -intercept is x -axis symmetry: y 18 x , which is not the y 18 x , so the graph is not symmetric with respect to the x -axis same as y -axis symmetry: y x 18 x , y 18 x , so the graph is not symmetric with respect to the y -axis which is not the same as Origin symmetry: y 18 x y 14 x , which is not the same as y 14 x , y 18 x , which is the same as y 18 x , so the graph is not symmetric with respect to the origin so the graph is symmetric with respect to the origin Z Z M M Y Y INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Solution Manual for Trigonometry 2nd Edition by Stewart NOT FOR SALE Full file 16 at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Chapter 1: Functions unctions and Graphs Gr 65 y x2 x 4 3 2 1 66 y y x 4 7 3 2 1 7 y 5 8 9 8 5 y º x 9 x º x o3 , so the x -intercepts are and 3 , and x º y 9 , so the y -intercept is 9 x2 y º x2 x2 º x o3 , so the x -intercepts are 3 and , º y , so the y -intercept is and x x -axis symmetry: y x , which is x -axis symmetry: y x , which is not the same as y x , so the graph is not symmetric with respect to the x -axis not the same as y x , so the graph is not symmetric with respect to the x -axis y -axis symmetry: y x y x , so the graph is symmetric with respect to the y -axis Origin symmetry: y x 9 y x , which is not the same as y x , so the graph is not symmetric with y -axis symmetry: y x x , so the graph is symmetric with respect to the y axis Origin symmetry: y x y x , which is not the same as y x , so the graph is not symmetric with respect to the origin respect to the origin Z Z M Y M Y INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Solution Manual for Trigonometry 2nd Edition by Stewart NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Trigonometry, T Trigo rigo 2e 17 y 67 xy x 4 y x 68 y y x 4 1 15 1 2 4 3 2 12 4 2 1 1 1 8 4 x y º x x 4 so the x -intercept is 4 , and x º y y or x º , which is impossible, so this equation has no x -intercept and no y -intercept x -axis symmetry: x y xy , which is not the same as xy , so the graph is not symmetric with respect to the x axis y -axis symmetry: x y , so the y -intercept is Since we are graphing real numbers and x is defined to be a nonnegative number, the equation is not symmetric with respect to the x -axis nor with respect to the y -axis Also, the equation is not symmetric with respect to the origin Z M Y xy , which is not the same as xy , so the graph is not symmetric with respect to the y axis Origin symmetry: x y xy , so the graph is symmetric with respect to the origin Z M Y INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Solution Manual for Trigonometry 2nd Edition by Stewart NOT FOR SALE Full file 18 at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Chapter 1: Functions unctions and Graphs Gr 69 y x Since the radicand (the inside of the square root) cannot be negative, we must have x2 p x2 b x 2 1 y 0 x b2 3 x2 y 0 º 0 x x º x o2 , so the x -intercepts are 2 and , and x , so the y intercept is Since y p , the graph is not symmetric with respect to the x -axis y -axis symmetry: º y x x , so the graph is symmetric with respect to the y -axis Also, since y p the graph is not symmetric with respect to y the origin Z 70 Since the radicand (the expression inside the square root symbol) cannot be negative, we must have x p x2 b x b So 2 b x b is the only portion of the x -axis where this equation is defined y x 2 1 4 y º x2 x x º x o2 , so the x -intercepts are 2 and , and x º y 2 , so the y -intercept is 2 x -axis symmetry: Since y b , this graph is not symmetric with respect to the x -axis y -axis symmetry: y x x , so the graph is symmetric with respect to the y -axis Origin symmetry: Since y b , the graph is not symmetric with respect to the origin Z M Y M Y INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Solution Manual for Trigonometry 2nd Edition by Stewart NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Trigonometry, T Trigo rigo 2e 19 71 Solve for x in terms of y : x y2 x y2 x 12 5 5 12 y 4 3 2 1 72 Since x y is solved for x in terms of y , we insert values for y and find the corresponding values of x y x 27 3 8 2 1 1 0 1 27 3 y º x 02 x , so the x -intercept is , and x º y º y o2 , so the y intercepts are 2 and x -axis symmetry: x y x y , so the graph is symmetric with respect to the x -axis y -axis symmetry: x y x y , which is not the same, so the graph is not symmetric with respect to the y -axis Origin symmetry: x y 4 x y , which is not the same as x y , so the graph is not symmetric with y º x , so the x intercept is , and x º y , so the y -intercept is y3 º x -axis symmetry: x y y , which is not the same as x y , so the graph is not symmetric with respect to the x -axis y -axis symmetry: x y x y , which is not the same as x y , so the graph is not symmetric with respect to the y axis Origin symmetry: x y x y x y , so the graph is symmetric with respect to the origin Z respect to the origin Z M Y M Y INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Solution Manual for Trigonometry 2nd Edition by Stewart NOT FOR SALE Full file 20 at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Chapter 1: Functions unctions and Graphs Gr x y Here we insert values of y and find the corresponding value of x 73 y 16 x y x 3 65 2 1 15 16 15 65 74 y º 16 x º x 16 º x º x o2 , so the x intercepts are o2 , and so x º x -axis symmetry: y 16 x y 16 x , which is not the same as y 16 x , so the graph is not symmetric with respect to the x -axis y -axis symmetry: y 16 x 16 x , so the graph is symmetric with respect to the y -axis Origin symmetry: y 16 x is , and x º 0 y y 0, so the y -intercept is x -axis symmetry: x y y , so the graph is symmetric with respect to the x -axis y axis symmetry: Since x p , the graph is not symmetric with respect to the y -axis Origin symmetry: Since x p , the graph is not symmetric with respect to the origin Z y 16 x , which is not the same as y 3 2 1 y º x , so the x -intercept y 16 04 16 , so the y -intercept is 16 x 1 y 16 x , so the graph is not symmetric with M Y respect to the origin Z M Y INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Solution Manual for Trigonometry 2nd Edition by Stewart Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Trigonometry, 2e 21 Trigo 75 y 4 x 76 y x 6 2 4 2 2 2 y º 4 x x º x o4 , so the x -intercepts are 4 and , and x º y , so the y -intercept is x -axis symmetry: y x y 4 x , which is not the same as y x , so the graph is not symmetric with respect to the x -axis y -axis symmetry: y x x , so the graph is symmetric with respect to the y axis Origin symmetry: y x y 4 x ,which is not the same as y x , so the graph is not symmetric with respect to the origin y 4x y x 6 10 4 2 2 10 y º 4x x º x , so the x -intercept is , and x º y , so the y -intercept is x -axis symmetry: y x x y x , so the graph is not symmetric with respect to the x -axis y -axis symmetry: y x , which is not the same as y x , which is not the same as y x , so the graph is not symmetric with respect to the y -axis Origin symmetry: y x y x , which is not the same as y x , so the graph is not symmetric with Z respect to the origin Z M Y M Y INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Solution Manual for Trigonometry 2nd Edition by Stewart Full file 22 at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Chapter 1: Functions unctions and Graphs Gr y x x y x x , which is not the same as y x x , so the graph is not symmetric with respect to the x -axis 77 x -axis symmetry: y -axis symmetry: y x x x x , so the graph is symmetric with respect to the y axis Origin symmetry: y x x y x x , which is not the same as y x x , so the graph is not symmetric with respect to the origin 78 x -axis symmetry: x y y y y , so the graph is symmetric with respect to the x axis y -axis symmetry: x y y , which is not the same as x y y , so the graph is not symmetric with respect to the y -axis Origin symmetry: x y y x y y , which is not the same as x y y , so the graph is not symmetric with respect to the origin 79 x -axis symmetry: x y x y x 2y xy , which is not the same as x 2y xy , so the graph is not symmetric with respect to the x -axis y -axis symmetry: x y x y x 2y xy , which is not the same as x 2y xy , so the graph is not symmetric with respect to the y -axis Origin symmetry: 2 x y x y x 2y xy , so the graph is symmetric with respect to the origin 80 x -axis symmetry: x y x y x 4y x 2y , so the graph is symmetric with respect to the x -axis y -axis symmetry: x y x y x 4y x 2y , so the graph is symmetric with respect to the y -axis Origin symmetry: 4 x y 2 x y x 4y x 2y , so the graph is symmetric with respect to the origin 81 x -axis symmetry: y x 10x y x 10x , which is not the same as y x 10x , so the graph is not symmetric with respect to the x -axis y -axis symmetry: y x 10 x y x 10x , which is not the same as y x 10x , so the graph is not symmetric with respect to the y -axis Origin symmetry: y x 10 x y x 10x y x 10x , so the graph is symmetric with respect to the origin INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Solution Manual for Trigonometry 2nd Edition by Stewart NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Trigonometry, T Trigo rigo 2e 23 82 x -axis symmetry: y x x y x x , which is not the same as y x x , so the graph is not symmetric with respect to the x -axis y -axis symmetry: y x x y x x , so the graph is symmetric with respect to the y -axis Note that x x Origin symmetry: y x x y x x y x x , which is not the same as y x x , so the graph is not symmetric with respect to the origin 83 Symmetric with respect to the y -axis 84 Symmetric with respect to the x -axis Z Z Y 85 Symmetric with respect to the origin Y 86 Symmetric with respect to the origin Z Z Y 87 x y has center 0, and radius 88 Y x y has center 0, and radius Z Z M Y M Y INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Solution Manual for Trigonometry 2nd Edition by Stewart NOT FOR SALE Full file 24 at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart Chapter 1: Functions unctions and Graphs Gr 89 x y 16 has center 3, 90 x y has center and radius 0,2 and radius Z Z M M 2 x y 3, and radius 91 Y Y 2 x y 1, 2 and radius 25 has center 92 Z 36 has center Z M Y M Y 93 Using h , k 1 , and r , we get x 2 2 x 1 y 4 82 y 64 95 The equation of a circle centered at the origin is This gives y 1 32 y 94 Using h 1 , k 4 , and r , we get x x 2 x y r Using the point 4, we solve for r r 16 49 65 r Thus, the equation of the circle is x y 65 96 Using h 1 and k , we get x 2 2 y r y r Next, using the point 4, 6 , we solve for r This gives 4 x x 1 6 r 130 r Thus, an equation of the circle is y 130 INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-2nd-Edition-by-Stewart ... https://TestbankDirect.eu /Solution- Manual- for- Trigonometry- 2nd- Edition- by- Stewart Solution Manual for Trigonometry 2nd Edition by Stewart NOT FOR SALE Full file 2at https://TestbankDirect.eu /Solution- Manual- for- Trigonometry- 2nd- Edition- by- Stewart. .. Stewart NOT FOR SALE Full file 2at https://TestbankDirect.eu /Solution- Manual- for- Trigonometry- 2nd- Edition- by- Stewart Chapter 1: Functions nctions and Graphs Gra 2, 1 10 The two points are (a) d ... the graph of an equation in x and y , then the equation is satisfied when we replace ? ? x by and y by We check whether This is false, so the point 2, is not on the graph of the equation