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King Fahd University of Petroleum and Minerals Prep -Year Math Program Math 002 - Term 153 Recitation (6.1) Question1 If πΌ is the least negative angle with coterminal angle of measure 39π 4 and π½ is the reference angle of the angle of measure 30 radian, then find πΌ + π½. Question2 Find the length of an arc that subtends a central angle of 40Λ 15 Μ in a circle of circumference 30Ο cm. Question3 If the arc length 4π 3 ππ subtends a central angle ΞΈ in a circle with diameter 12 ππ, find the degree measure of the angle ΞΈ. Question4 A rope is being wound around a drum of radius 5 ππ‘. How much rope will be wound if the drum is rotated through an angle of 120Λ. Question5 The radian measure of the reference angle of β2560Λ is A) 16π 9 B) β C) D) 2π 9 5π 18 2π 9 Question6 If a point P lies on a circle of center O(0,0) and radius 4 units and the radius OP π makes an angle of with π₯-axis, then the coordinates of P = 4 A) (1, β2) D) ( 1 , 1 ) β2 β2 B) (4, 4) E) (β2, β2) C) (2β2, 2β2) King Fahd University of Petroleum and Minerals Prep -Year Math Program Math 002 - Term 153 Recitation (6.2) Question1: Find the exact value of the following: β7π 1) cos ( 6 ) + sin ( 17π 3 5π ) + 3 tan ( 4 ) 2) csc(5Ο) 3)2 sin ( 19π 6 ) β cos(660Λ) tan ( 39π 4 β71π ) + sec ( 6 ). Question2 The Earth revolves on its axis once every 24 hr and its radius is 6.371 km. Find the linear speed of the earth. Question3 Each tire of a car has a radius of 40 cm. If the tires are rotating at 500 revolutions per minute, find the speed of the car in kilometers per hour. Question4 Two pulleys in the figure have radii of 15cm and 8 cm respectively. If the larger pulley rotates 50 times in a minute, then the angular speed of the smaller pulley in radians per second is A) 75π 4 B) Question5 πΆππ (20) = A) β cos(20 β 6π) B) cos 70 C) βcos 70 D) cos(20 β 6π) E) sin(20 β 6π) 25π 8 C) 75π 8 D) 25π 4 E) 375π 2 King Fahd University of Petroleum and Minerals Prep -Year Math Program Math 002 - Term 153 Recitation (6.3) Question1: a) Find the intervals in which the function π(π₯) = β|πππ ππ₯| is increasing and decreasing in the interval [0,4]. 1 ππ₯ b) Find the highest point of the function π(π₯) = β cos ( ) in the interval [0,4]. 5 2 Question2: 3 π₯ 2 3 a) For β3Ο β€ x β€ 3Ο, find the interval in which the function π(π₯) = β cos is above the π₯-axis. b) Find the number of intersection points of the graphs of π¦ = β|sin ππ₯| and π¦ = 1 1 3 2 2 4 β over the interval [ , ]. Question3: If πππ 3 = π and π ππ3 = π, then π β π = A) a positive real number. B) a negative real number. C) zero. D) undefined. Question4: The number of zeros of the function π(π₯) = β2 sin A) 1 B) 2 C) 3 D) 4 E) 5 4π₯ 3 in the interval [β 3π 3π 2 , 2 ] is: King Fahd University of Petroleum and Minerals Prep -Year Math Program Math 002 - Term 153 Recitation (6.4) Question1: If π and πΉ are the period and the phase shift respectively and π = [π, π] is the 1 range of the graph of π¦ = β1 + cos(3π₯ β 2π), then find π β πΉ + π + π 4 Question2: π₯ Find the number of π₯-intercepts of the function π(π₯) = 1 + β2 sin ( + π) in the 2 interval (β4π, 0). Question3: If π΄ is the amplitude, π is the period, π is the maximum value and m is the minimum value of the function π(π₯) = β3 sin(2ππ₯ β 1) + 5, then A) 3 B) 3 C) 5 11 D) 10 7 π΄+π π+π = E) 10 9 5 Question4: 1 ο°οΆ ο¦ Which one of the following is the graph of y ο½ cos 2 ο§ x ο« ο· over one period? 4 4οΈ ο¨ a ) b ) y c ) y x x d e) y y x x y x King Fahd University of Petroleum and Minerals Prep -Year Math Program Math 002 - Term 153 Recitation (6.5) Question1: Find the interval(s) in which the function π¦ = tan|π₯|, β 3π 2 β€π₯β€ 3π 2 , is above the π₯-axis. Question2: π₯ π a) Find all vertical asymptotes of the graph of π¦ = 3 tan ( β ), for β6π β€ π₯ β€ 3 6 6π. b) Find the number of vertical asymptotes of the graph of the function 1 π 7π 2 4 π¦ = πππ‘(2π₯ β 3π) in the interval [ , 4 ]. Question3: π Find the interval(s) in which the function π¦ = β2 tan (3π₯ + ) is increasing, 4 where β 3π 4 β€π₯β€ 7π 12 . Question4: π The intersection point(s) between the graph of π¦ = cot(2π₯ + ) and the x-axis 3 π over the interval ( , 12 A) 7π B) 12 4π 3 ): 13π C) 12 π 12 , 7π 12 D) 7π 13π 12 , 12 E) π 12 , 13π 12 Question5: The graph below can be represented by the trigonometric function A) f ο¨ x ο© ο½ ο 2 tan ο¦ο§ ο° ο¨4 xο« ο°οΆ ο· 4οΈ C) ο¦ο° οΆ f ο¨ x ο© ο½ 2 cot ο§ x ο« 1ο· ο¨4 οΈ E) f ο¨ x ο© ο½ 2 cot ο¨ x ο« 1ο© B) f ο¨ x ο© ο½ 2 tan ο¦ο§ ο° ο¨4 xο« ο°οΆ ο· 4οΈ y D) f ο¨ x ο© ο½ ο 2 tan ο¨ x ο« 1ο© x King Fahd University of Petroleum and Minerals Prep -Year Math Program Math 002 - Term 153 Recitation (6.6) Question1 π Find the range of the function π¦ = 2 β 3csc( π₯ + 4)? 2 Question2 Find the number of the intersection points of the graph of π¦ = |3π ππ 2π₯ 3 | and the line 9π y = 4 over the interval [0, ]? 4 Question3 Write a function for the given graph Question4 For π 2 β€π₯β€ 9π π₯ π , the graph of the function π¦ = csc ( β ) is decreasing in the 2 2 4 interval(s) a) 3π (2 , π π) ( , 2 5π d) ( , 2 5π 5π )βͺ (2 , 2 5π 2 9π 2 7π ) 2 π b) ( , 2 3π 7π ) βͺ (2 , 2 ) ) π 9π 2 2 e) ( , ) 9π 2 ) Question5 The graph of the function π¦ = β sec(2π₯ + π) + 2, where a) three π₯-intercepts b) three vertical asymptotes d) two vertical asymptotes e) four π₯ -intercepts Question6 How many intersection points are there between a) The graph of π¦ = π πππ₯ and the line π¦ = 0. b) The graph of π¦ = π πππ₯ +1 and the line π¦ = 0. β3π 4 β€π₯β€ 3π 4 has c) one π¦ -intercept