HW4sol - MAC1114 - Homework 4 Due Thursday, February 3 1....

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Unformatted text preview: MAC1114 - Homework 4 Due Thursday, February 3 1. Consider the equation y = 3 sin(2x − π ) + 1. 2π (a) What is the period? Period = b (b) What is the amplitude? = 2π 2 =π a=3 c (c) What is the phase shift? Phase shift = b (d) What is the vertical translation? d=1 = π 2 to the right. up. 2. State the equation of a cosine function with the following characteristics (i.e., your answer should be of the form a cos(bx − c) + d): period= 1, minimum value −1 and maximum value 0, phase shift right by 1. c = 2π 2π b hence a = 1 and that 2 cos(2πx − 2π ) − 1. the amplitude is 1 we get 2 = 1, c 3. Graph the equation b = 2π . c Since there is a phase shift right by 1, b = 2π = 1, so and the sign is negative. The minimum value of -1 and the maximum value of 0 tells us that Since the period is 1, there is a vertical shift down by y = 2 cos(πx − 3π ) − 1. 1 1, so d = −1. Putting this together ...
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