# Physics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion

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1 Physics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion Conceptual Questions 1) Which of Newton's laws best explains why motorists should buckle-up? A) the first law B) the second law C) the third law D) the law of gravitation 2) When you sit on a chair, the resultant force on you is A) zero. B) up. C) down. D) depending on your weight. 3) In the absence of an external force, a moving object will A) stop immediately. B) slow down and eventually come to a stop. C) go faster and faster. D) move with constant velocity. 4) When the rocket engines on the starship NO-PAIN-NO-GAIN are suddenly turned off, while traveling in empty space, the starship will A) stop immediately. B) slowly slow down, and then stop. C) go faster and faster. D) move with constant speed. 5) A rocket moves through empty space in a straight line with constant speed. It is far from the gravitational effect of any star or planet. Under these conditions, the force that must be applied to the rocket in order to sustain its motion is A) equal to its weight. B) equal to its mass. C) dependent on how fast it is moving. D) zero. 1

2 6) You are standing in a moving bus, facing forward, and you suddenly fall forward. You can imply from this that the bus's A) velocity decreased. B) velocity increased. C) speed remained the same, but it's turning to the right. D) speed remained the same, but it's turning to the left. Diff: 1 Type: BI Var: 2 Page Ref: Sec ) You are standing in a moving bus, facing forward, and you suddenly fall forward as the bus comes to an immediate stop. What force caused you to fall forward? A) gravity B) normal force due to your contact with the floor of the bus C) force due to friction between you and the floor of the bus D) There is not a force leading to your fall. Diff: 2 Type: BI Var: 1 Page Ref: Sec ) A constant net force acts on an object. Describe the motion of the object. A) constant acceleration B) constant speed C) constant velocity D) increasing acceleration 9) The acceleration of an object is inversely proportional to A) the net force acting on it. B) its position. C) its velocity. D) its mass. Diff: 1 Type: BI Var: 2 Page Ref: Sec ) A net force F accelerates a mass m with an acceleration a. If the same net force is applied to mass 2m, then the acceleration will be A) 4a. B) 2a. C) a/2. D) a/4. Diff: 1 Type: BI Var: 2 Page Ref: Sec ) A net force F acts on a mass m and produces an acceleration a. What acceleration results if a net force 2F acts on mass 4m? A) a/2 B) 8a C) 4a D) 2a Diff: 1 Type: BI Var: 2 Page Ref: Sec

3 12) If you blow up a balloon, and then release it, the balloon will fly away. This is an illustration of A) Newton's first law. B) Newton's second law. C) Newton's third law. D) Galileo's law of inertia. 13) Two cars collide head-on. At every moment during the collision, the magnitude of the force the first car exerts on the second is exactly equal to the magnitude of the force the second car exerts on the first. This is an example of A) Newton's first law. B) Newton's second law. C) Newton's third law. D) Newton's law of gravitation. 14) If you exert a force F on an object, the force which the object exerts on you will A) depend on whether or not the object is moving. B) depend on whether or not you are moving. C) depend on the relative masses of you and the object. D) always be F. 15) Action-reaction forces A) sometimes act on the same object. B) always act on the same object. C) may be at right angles. D) always act on different objects. Diff: 1 Type: MC Var: 1 Page Ref: Sec ) Action-reaction forces are A) equal in magnitude and point in the same direction. B) equal in magnitude but point in opposite directions. C) unequal in magnitude but point in the same direction. D) unequal in magnitude and point in opposite directions Diff: 1 Type: MC Var: 1 Page Ref: Sec ) A 20-ton truck collides with a 1500-lb car and causes a lot of damage to the car. Since a lot of damage is done on the car A) the force on the truck is greater then the force on the car. B) the force on the truck is equal to the force on the car. C) the force on the truck is smaller than the force on the car. D) the truck did not slow down during the collision. Diff: 1 Type: MC Var: 1 Page Ref: Sec

4 18) An object of mass m sits on a flat table. The Earth pulls on this object with force mg, which we will call the action force. What is the reaction force? A) The table pushing up on the object with force mg. B) The object pushing down on the table with force mg. C) The table pushing down on the floor with force mg. D) The object pulling upward on the Earth with force mg. Diff: 2 Type: BI Var: 1 Page Ref: Sec ) A child's toy is suspended from the ceiling by means of a string. The Earth pulls downward on the toy with its weight force of 8.0 N. If this is the "action force," what is the "reaction force"? A) The string pulling upward on the toy with an 8.0-N force. B) The ceiling pulling upward on the string with an 8.0-N force. C) The string pulling downward on the ceiling with an 8.0-N force. D) The toy pulling upward on the Earth with an 8.0-N force. Diff: 2 Type: BI Var: 1 Page Ref: Sec ) A golf club hits a golf ball with a force of 2400 N. The golf ball hits the club with a force A) slightly less than 2400 N. B) exactly 2400 N. C) slightly more than 2400 N. D) close to 0 N. 21) Your bat hits the ball pitched to you with a 1500-N instantaneous force. The ball hits the bat with an instantaneous force, whose magnitude is A) somewhat less than 1500 N. B) somewhat greater than 1500 N. C) exactly equal to 1500 N. D) essentially zero. 22) State Newton's three laws. Answer: Newton's first law: Every object continues in its state of rest, or of uniform velocity in a straight line, as long as no net force acts on it. Newton's second law: The acceleration of an object is directly proportional to the net force acting on it, and is inversely proportional to its mass. The direction of the acceleration is in the direction of the net force acting on the object. Newton's third law: Whenever one object exerts a force on a second object, the second exerts an equal force in the opposite direction on the first. Diff: 1 Type: ES Var: 1 Page Ref: Sec ) Mass and weight A) both measure the same thing. B) are exactly equal. C) are two different quantities. D) are both measured in kilograms. Diff: 1 Type: MC Var: 1 Page Ref: Sec

5 24) The acceleration due to gravity is lower on the Moon than on Earth. Which of the following is true about the mass and weight of an astronaut on the Moon's surface, compared to Earth? A) Mass is less, weight is same. B) Mass is same, weight is less. C) Both mass and weight are less. D) Both mass and weight are the same. Diff: 2 Type: BI Var: 1 Page Ref: Sec ) An example of a force which acts at a distance is A) tension. B) weight. C) static friction. D) kinetic friction. Diff: 1 Type: BI Var: 1 Page Ref: Sec ) Who has a greater weight to mass ratio, a person weighing 400 N or a person weighing 600 N? A) the person weighing 400 N B) the person weighing 600 N C) Neither; their ratios are the same. D) The question can't be answered; not enough information is given. Diff: 1 Type: BI Var: 1 Page Ref: Sec ) A stone is thrown straight up. At the top of its path, the net force acting on it is A) greater than its weight. B) greater than zero, but less than its weight. C) instantaneously equal to zero. D) equal to its weight. Diff: 1 Type: BI Var: 1 Page Ref: Sec ) A 20-N weight and a 5.0-N weight are dropped simultaneously from the same height. Ignore air resistance. Compare their accelerations. A) The 20 N weight accelerates faster because it is heavier. B) The 20 N weight accelerates faster because it has more inertia. C) The 5.0 N weight accelerates faster because it has a smaller mass. D) They both accelerate at the same rate because they have the same weight to mass ratio. Diff: 2 Type: BI Var: 1 Page Ref: Sec ) A brick and a feather fall to the earth at their respective terminal velocities. Which object experiences the greater force of air friction? A) the feather B) the brick C) Neither, both experience the same amount of air friction. D) It cannot be determined because there is not enough information given. Diff: 2 Type: BI Var: 1 Page Ref: Sec

6 30) An object of mass m is hanging by a string from the ceiling of an elevator. The elevator is moving up at constant speed. What is the tension in the string? A) less than mg B) exactly mg C) greater than mg D) cannot be determined without knowing the speed Diff: 2 Type: BI Var: 1 Page Ref: Sec ) An object of mass m is hanging by a string from the ceiling of an elevator. The elevator is moving upward, but slowing down. What is the tension in the string? A) less than mg B) exactly mg C) greater than mg D) zero Diff: 2 Type: BI Var: 1 Page Ref: Sec ) The force that keeps you from sliding on an icy sidewalk is A) weight. B) kinetic friction. C) static friction. D) normal force. 33) It's more difficult to start moving a heavy carton from rest than it is to keep pushing it with constant velocity, because A) the normal force is greater when the carton is at rest. B) <. C) initially, the normal force is not perpendicular to the applied force. D) <. Diff: 1 Type: BI Var: 1 Page Ref: Sec ) A horizontal force accelerates a box from rest across a horizontal surface (friction is present) at a constant rate. The experiment is repeated, and all conditions remain the same with the exception that the horizontal force is doubled. What happens to the box's acceleration? A) It increases to more than double its original value. B) It increases to exactly double its original value. C) It increases to less than double its original value. D) It increases somewhat. 35) A packing crate slides down an inclined ramp at constant velocity. Thus we can deduce that A) a frictional force is acting on it. B) a net downward force is acting on it. C) it may be accelerating. D) it is not acted on by appreciable gravitational force. Diff: 1 Type: BI Var: 1 Page Ref: Sec

7 36) A block of mass M slides down a frictionless plane inclined at an angle θ with the horizontal. The normal reaction force exerted by the plane on the block is A) Mg. B) Mg sin θ. C) Mg cos θ. D) zero, since the plane is frictionless. Diff: 1 Type: BI Var: 1 Page Ref: Sec ) A block of mass M slides down a frictionless plane inclined at an angle θ with the horizontal. The normal reaction force exerted by the plane on the block is directed A) parallel to the plane in the same direction as the movement of the block. B) parallel to the plane in the opposite direction as the movement of the block C) perpendicular to the plane. D) toward the center of the Earth. Diff: 1 Type: BI Var: 1 Page Ref: Sec ) A block of mass M slides down a frictionless plane inclined at an angle θ with the horizontal. The gravitational force is directed A) parallel to the plane in the same direction as the movement of the block. B) parallel to the plane in the opposite direction as the movement of the block C) perpendicular to the plane. D) toward the center of the Earth. Diff: 1 Type: BI Var: 1 Page Ref: Sec ) Two toy cars (16 kg and 2.0 kg) are released simultaneously on an inclined plane that makes an angle of 30 with the horizontal. Make a statement which best describes their acceleration after being released. A) The 16-kg car accelerates 8 times faster than the 2.0-kg car. B) The 2.0-kg car accelerates 8 times faster than the 16-kg car. C) Both cars accelerate at the same rate. D) none of the above Quantitative Problems 1) An object sits on a frictionless surface. A 16-N force is applied to the object, and it accelerates at 2.0 m/s2. What is the mass of the object? A) 4.0 kg B) 8.0 kg C) 32 kg D) 78 N Diff: 1 Type: BI Var: 4 Page Ref: Sec ) A sports car of mass 1000 kg can accelerate from rest to 27 m/s in 7.0 s. What is the average forward force on the car? A) N B) N C) N D) N 7

8 Diff: 1 Type: BI Var: 1 Page Ref: Sec ) Starting from rest, a 4.0-kg body reaches a speed of 8.0 m/s in 2.0 s. What is the net force acting on the body? A) 4.0 N B) 8.0 N C) 16 N D) 32 N Diff: 2 Type: BI Var: 1 Page Ref: Sec ) An antitank weapon fires a 3.00-kg rocket which acquires a speed of 50.0 m/s after traveling 90.0 cm down a launching tube. Assuming the rocket was accelerated uniformly, what is the average force acted on it? A) N B) N C) N D) N Diff: 2 Type: BI Var: 1 Page Ref: Sec ) If you push a 4.0-kg mass with the same force that you push a 10-kg mass from rest, A) the 10-kg mass accelerates 2.5 times faster than the 4.0-kg mass. B) the 4.0-kg mass accelerates 2.5 times faster than the 10-kg mass. C) both masses accelerate at the same rate. D) None of the above is true. Diff: 1 Type: BI Var: 1 Page Ref: Sec ) What is the mass of a person who weighs 110 lb? A) 50 kg B) 55 kg C) 110 kg D) 242 kg Diff: 1 Type: BI Var: 5 Page Ref: Sec ) What is the mass of an object that weighs 250 N on the surface of the Earth where the acceleration due to gravity is 9.80 m/s2? A) 250 kg B) 24.5 kg C) 25.5 kg D) 2,450 kg Diff: 1 Type: BI Var: 5 Page Ref: Sec ) An object has a mass of 60 kg on the Earth. What is the mass of the object on the surface of the Moon where the acceleration due to gravity is only 1/6 of that on the Earth? A) 6.0 kg B) 10 kg C) 60 kg D) 360 kg Diff: 1 Type: BI Var: 1 Page Ref: Sec

9 9) Object A weighs 40 N on Earth, and object B weighs 40 N on the Moon. The Moon's gravity is one sixth of Earth's. Compare the masses of the objects. A) A has 6 times the mass of B. B) B has 6 times the mass of A. C) A and B have equal mass. D) The situation as stated is impossible. Diff: 2 Type: BI Var: 1 Page Ref: Sec ) Sue and Sean are having a tug-of-war by pulling on opposite ends of a 5.0-kg rope. Sue pulls with a 15-N force. What is Sean's force if the rope accelerates toward Sue at 2.0 m/s2? A) 3.0 N B) 5.0 N C) 25 N D) 50 N Diff: 2 Type: BI Var: 1 Page Ref: Sec ) A stack of books rests on a level frictionless surface. A force F acts on the stack, and it accelerates at 3.0 m/s2. A 1.0 kg book is then added to the stack. The same force is applied, and now the stack accelerates at 2.0 m/s2. What was the mass of the original stack? A) 1.0 kg B) 2.0 kg C) 3.0 kg D) none of the above Diff: 2 Type: BI Var: 1 Page Ref: Sec ) A person of weight 480 N stands on a scale in an elevator. What will the scale be reading when the elevator is accelerating downward at 4.00 m/s2? A) 196 N B) 284 N C) 676 N D) 480 N Diff: 2 Type: BI Var: 2 Page Ref: Sec ) A person on a scale rides in an elevator. If the mass of the person is 60.0 kg and the elevator accelerates downward with an acceleration of 4.90 m/s2, what is the reading on the scale? A) 147 N B) 294 N C) 588 N D) 882 N Diff: 2 Type: BI Var: 1 Page Ref: Sec

10 14) A person on a scale rides in an elevator. If the mass of the person is 60.0 kg and the elevator accelerates upward with an acceleration of 4.90 m/s2, what is the reading on the scale? A) 147 N B) 294 N C) 588 N D) 882 N Diff: 2 Type: BI Var: 1 Page Ref: Sec ) Two horizontal forces act on a 5.0-kg mass. One force has a magnitude of 8.0 N and is directed due north. The second force toward the east has a magnitude of 6.0 N. What is the acceleration of the mass? A) 1.6 m/s2 due north B) 1.2 m/s2 due east C) 2.0 m/s2 at 53 N of E D) 2.0 m/s2 at 53 m E of N Diff: 1 Type: BI Var: 1 Page Ref: Sec ) An object of mass 6000 kg rests on the flatbed of a truck. It is held in place by metal brackets that can exert a maximum horizontal force of 9000 N. When the truck is traveling 15 m/s, what is the minimum stopping distance if the load is not to slide forward into the cab? A) 15 m B) 30 m C) 75 m D) 150 m 17) An object of mass 6000 kg rests on the flatbed of a truck. It is held in place by metal brackets that can exert a maximum horizontal force of 9000 N. When the truck is traveling 15 m/s, what is the minimum stopping time if the load is not to slide forward into the cab? A) 5.0 s B) 10 s C) 13 s D) 23 s 10

11 FIGURE ) In the Atwood machine shown in Fig. 4-1, if M = 0.60 kg and m = 0.40 kg, what is the magnitude of the acceleration of the system? (Ignore friction and the mass of the pulley.) A) 5.3 m/s2 B) 3.9 m/s2 C) 2.0 m/s2 D) 0.98 m/s2 19) In the Atwood machine shown in Fig. 4-1, if M = 0.60 kg and m = 0.40 kg, what is the tension in the string? (Ignore friction and the mass of the pulley.) A) 3.1 N B) 4.7 N C) 7.1 N D) 7.5 N 20) A student pulls a box of books on a smooth horizontal floor with a force of 100 N in a direction of 37 above the horizontal. If the mass of the box and the books is 40.0 kg, what is the acceleration of the box? A) 1.5 m/s2 B) 1.9 m/s2 C) 2.0 m/s2 D) 3.3 m/s2 11

12 21) A student pulls a box of books on a smooth horizontal floor with a force of 100 N in a direction of 37.0 above the horizontal. If the mass of the box and the books is 40.0 kg, what is the normal force on the box? A) 292 N B) 312 N C) 332 N D) 392 N FIGURE ) A traffic light of weight 100 N is supported by two ropes as shown in Fig What are the tensions in the ropes? A) 50 N B) 63 N C) 66 N D) 83 N 23) In Fig. 4-2, if the tensions in the ropes are 50 N, what is the mass of the traffic light? A) 3.1 kg B) 4.1 kg C) 6.1 kg D) 8.1 kg 12

13 FIGURE ) Two boxes of masses m and 2m are in contact with each other on a frictionless surface. (See Fig. 4-3.) What is the acceleration of the more massive box? A) F/m B) F/(2m) C) F/(3m) D) F/(4m) 25) Two boxes of masses m and 2m are in contact with each other on a frictionless surface. (See Fig. 4-3.) What is the net force on the more massive box? A) 2/3 F B) F C) 3/2 F D) 2F FIGURE ) Two boxes of masses m and 2m are connected by a rope. (See Fig. 4-4.) If the forward force on the more massive box is F, what is the tension in the connecting rope? A) 3F B) F C) F/2 D) F/3 13

14 27) Two boxes of masses m and 2m are connected by a rope. (See Fig. 4-4.) If the forward force on the more massive box is F, what is the acceleration of the less massive box? A) F/(3m) B) F/(2m) C) F/m D) 2F/m FIGURE ) Two boxes are connected by a cord running over a pulley as shown in Fig Box I of mass 8.0 kg rest on the top of the table; the coefficient of kinetic friction between box I and the table is Box II has a mass of 15.0 kg. (a) Draw the free-body diagrams for the two boxes, identifying all of the forces acting on each of the masses. (b) Calculate the acceleration of the system. (c) Calculate the tension in the cord. Answer: (a) Box one is acted on by the force of gravity in a downward direction, the normal force due to the table top in an upward direction, the tension in the string toward the right, and the force of friction due to the table top toward the left. Box two is acted on by the force of gravity in a downward direction and the tension in the string in an upward direction. (b) 6.1 m/ (c) 56 N Diff: 2 Type: ES Var: 1 Page Ref: Sec ) The coefficient of static and kinetic frictions between a 3.0-kg box and a desk are 0.40 and 0.30, respectively. What is the net force on the box when a 15 N horizontal force is applied to the box? A) 6.2 N B) 12 N C) 8.8 N D) zero Diff: 1 Type: BI Var: 2 Page Ref: Sec

15 30) The coefficients of static and kinetic frictions for plastic on wood are 0.50 and 0.40, respectively. How much horizontal force would you need to apply to a 3.0 N plastic calculator to start it moving from rest? A) 0.15 N B) 1.2 N C) 1.5 N D) 2.7 N Diff: 1 Type: BI Var: 1 Page Ref: Sec ) An object slides on a level surface in the +x direction. It slows and comes to a stop with a constant acceleration of m/s2. What is the coefficient of kinetic friction between the object and the floor? A) 0.25 B) 0.50 C) 4.9 D) Impossible to determine without knowing the mass of the object. 32) A 10-kg box sitting on a horizontal surface is pulled by a 5.0-N force. A 3.0-N friction force retards the motion. What is the acceleration of the object? A) 0.20 m/s2 B) 0.30 m/s2 C) 0.50 m/s2 D) 5.0 m/s2 33) A horizontal force of 5.0 N accelerates a 4.0-kg mass, from rest, at a rate of 0.50 m/s2 in the positive direction. What friction force acts on the mass? A) 2.0 N B) 3.0 N C) 4.0 N D) 5.0 N 34) During a hockey game, a puck is given an initial speed of 10 m/s. It slides 50 m on the ice before it stops. What is the coefficient of kinetic friction between the puck and the ice? A) B) 0.10 C) 0.11 D)

16 35) During the investigation of a traffic accident, police find skid marks 90.0 m long. They determine the coefficient of friction between the car's tires and the roadway to be for the prevailing conditions. Estimate the speed of the car when the brakes were applied. A) 9.49 m/s B) 21.0 m/s C) 29.7 m/s D) 42.0 m/s FIGURE ) Two boxes of masses m and 3m are stacked. (See Fig. 4-6.) The surface between the more massive box and the horizontal surface is smooth and the surface between the boxes is rough. If the less massive box does not slide on the more massive box, what is the static friction force on the less massive box? A) F B) F/2 C) F/3 D) F/4 Diff: 3 Type: BI Var: 1 Page Ref: Sec ) Two boxes of masses m and 3m are stacked. (See Fig. 4-6.) The surface between the more massive box and the horizontal surface is smooth and the surface between the boxes is rough. If the less massive box does not slide on the more massive box, what is the coefficient of static friction between the boxes? A) F/(4mg) B) F/(3mg) C) F/(2mg) D) F/(mg) Diff: 3 Type: BI Var: 1 Page Ref: Sec

17 38) An object is on a frictionless inclined plane. The plane is inclined at an angle of 30 with the horizontal. What is the object's acceleration? A) 0.50 g B) 0.56 g C) 0.87 g D) 1.0 g 39) A 10-kg mass slides down a flat hill that makes an angle of 10 with the horizontal. If friction is negligible, what is the resultant force on the sled? A) 1.7 N B) 17 N C) 97 N D) 98 N 40) A mass is placed on a smooth inclined plane with an angle of 37 to the horizontal. If the inclined plane is 5.0- m long, how long does it take for the mass to reach the bottom of the inclined plane after it is released from rest? A) 1.3 s B) 1.2 s C) 1.1 s D) 1.0 s 41) A block lies on a smooth inclined plane tilted at an angle of 35 to the horizontal. (a) Draw the free-body diagram for the block. (b) Determine the block's acceleration as it slides down the inclined plane. (c) If the block started from rest 8.5 m up the incline from its base, determine the block's speed when it reaches the bottom of the incline. (d) How long did it take the block to reach the bottom of the inclined plane? Answer: (a) The block is acted on by the force of gravity directed downward and the normal force due to the inclined plane directed perpendicular to the inclined surface. (b) 5.6 m/ (c) 9.7 m/s (d) 1.7 s Diff: 2 Type: ES Var: 1 Page Ref: Sec ) A wooden block slides directly down an inclined plane, at a constant velocity of 6.0 m/s. What is the coefficient of kinetic friction, if the plane makes an angle of 25 with the horizontal? A) 0.47 B) 0.42 C) 0.37 D)

18 43) An object with a mass m slides down a rough 37 inclined plane where the coefficient of kinetic friction is What is the acceleration of the object? A) 4.3 m/s2 B) 5.9 m/s2 C) 6.6 m/s2 D) 7.8 m/s2 Diff: 3 Type: BI Var: 1 Page Ref: Sec ) An object with a mass m slides down a rough 37 inclined plane where the coefficient of kinetic friction is If the plane is 10 m long and the mass starts from rest, what will be its speed at the bottom of the plane? A) 12 m/s B) 11 m/s C) 9.7 m/s D) 9.3 m/s Diff: 3 Type: BI Var: 1 Page Ref: Sec ) A bulldozer drags a log weighing 500 N along a rough surface. The cable attached to the log makes an angle of 30.0 with the ground. The coefficient of static friction between the log and the ground is What minimum tension is required in the cable in order for the log to begin to move? A) 224 N B) 268 N C) 289 N D) 500 N Diff: 3 Type: BI Var: 1 Page Ref: Sec ) A 25.0-kg box is released from rest on a rough inclined plane tilted at an angle of 33.5 to the horizontal. The coefficient of kinetic friction between the box and the inclined plane is (a) Draw the free-body diagram for the box. (b) Determine the force of kinetic friction acting on the box. (c) Determine the acceleration of the box as it slides down the inclined plane. Answer: (a) The box is acted on by the force of gravity directed downward, the normal force due to the inclined plane directed perpendicular to the surface of the incline, and the force of friction due to the inclined plane directed parallel to the inclined surface in the direction opposite of the motion. (b) 40.9 N (c) 3.77 m/ Diff: 3 Type: ES Var: 1 Page Ref: Sec ) An object is placed on an inclined plane. The angle of incline is gradually increased until the object begins to slide. The angle at which this occurs is θ. What is the coefficient of static friction between the object and the plane? A) sin θ B) cos θ C) tan θ D) 1/tan θ Diff: 3 Type: BI Var: 1 Page Ref: Sec

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