Pre-Calculus 30 Name: Unit 6 - Hand-in Assignment Date: 6.2 - Angles in Standard Position and Arc Length 18 a) What is the length of the arc that subtends a central angle of -3350 in a circle with a radius of 7 units? (2 marks) b) In a circle with radius 3 units, the length of the arc that subtends a positive central angle of 0 is 61 12 it units. What is the measure of 0 in degrees? (2 marks) c) An arc with length , 7 units subtends a central angle of 215' in a circle. Determine the radius of the circle. (2 marks) d) A Ferris wheel has diameter 42 m. Through what distance does a chair on the wheel travel when the wheel rotates 160'? (2 marks) 6.3 - Radian Measure /6 a) Determine the measures of all angles that are coterminal with an angle of - it in the domain I S 854x. (2 marks) b) Determine the exact value of csco -15x . (2 marks) c) P(-4,6) is a terminal point of angle 0 in standard position. Determine all possible measures of 0 in the domain -4x 5 05 0. Give the answers to the nearest tenth of a radian. (2 marks)Pre-Calculus 30 Name: Unit 6 - Hand-in Assignment Date: 6.4 - Graphs of Trigonometric Functions 18 a) Determine the characteristics of this function. Determine an equation as a sine function and as a cosine function. (4 marks) b) Determine the characteristics of this function. Determine an equation. (4 marks) 6.5 - Trigonometric Functions /18 a) Graph y = cos x+ 2. Identify the amplitude, period, general expression for the zeros, general equation for the asymptotes, domain of the function, and range of the function. (6 marks)Image T Pre-Calculus 30 Name: Unit 6 - Hand-in Assignment Date: 6.7 - Applications of Sinusoidal Functions 18 a) These data show the fraction of the moon that was visible at midnight, Mountain Standard Time, on alternate days in February, 2012. Graph the data, then write an equation of a sinusoidal function that models these data. (4 marks) Day Visible Fraction 0.61 3 0.78 5 0.92 7 0.99 0.6 9 0.97 Visible Fraction 11 0.85 13 0.66 15 0.44 0.2 17 0.23 19 0.08 12 16 20 24 28 32 21 0.01 Day 23 0.02 25 0.11 27 0.25 29 0.43 b) Suppose the function y - 19 cos (x - 3.5) + 24 models the height, y metres, of a seat on a Ferris wheel at any time x minutes after the wheel begins to rotate. After how many minutes is the seat at the top of the wheel for the first time? (4 marks)6.6- Combining Transformations of Sinusoidal Functions /6 Sketch the graph of y = 3 sin -3kin (3- - 2. Describe these characteristics of the function: amplitude, period, phase shift, equation of the midline, domain, and range (6 marks)