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Part of a roller coaster track is a sinusoidal function. The lowest point of the track is 6 feet above the ground and the highest point is 88 feet above the ground. The highest and lowest points of the track are separated 150 feet horizontally as shown below. 88 ft 6t 150 1) What is the amplitude of the function? 2) What is the midline/vertical shift of the function? [Hint: (highest point + lowest point)/2]: 3) What is its period?

Part of a roller coaster track is a sinusoidal function. The lowest point of the track is 6 feet above the ground and the highest point is 88 feet above the ground. The highest and lowest points of the track are separated 150 feet horizontally as shown below. 88 ft 6t 150 1) What is the amplitude of the function? 2) What is the midline/vertical shift of the function? [Hint: (highest point + lowest point)/2]: 3) What is its period?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 59E
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Part of a roller coaster track is a sinusoidal function. The lowest point of the track is 6 feet above the ground and the highest point is 88 feet above the ground. The highest and lowest points of the track are separated 150 feet horizontally as shown below. 88 ft 6 ft 0 150 1) What is the amplitude of the function? 2) What is the midline/vertical shift of the function? [Hint: (highest point + lowest point)/2] 3) What is its period? 4) What is the phase shift for a cosine function? 5) What is the phase shift for a sine function? 6) What is the cosine equation for this function? 7) What is the sine equation for this function? 150 75 :: 42 #300 #41 150 ft to the right :: 225 ft to the right 42 44 300 ft to the right :: 0 ft to the right :: y = 44 cos(x) + 47 :: y = 41 cos(x) + 47 :: y = 41 cos(x) + 47 :: y = 41 sin ( - 225) + 47 y = 41 sin(x - 300) + 47 y = 41 sin :: 250 ft to the right :: 1 ft to the right #47 #91 y = 44 cos(x) + 41 :: y = 44 sin (225) + 41 :: y = 44 sin 150(150) + 47 (300) + 47
Transcribed Image Text:Part of a roller coaster track is a sinusoidal function. The lowest point of the track is 6 feet above the ground and the highest point is 88 feet above the ground. The highest and lowest points of the track are separated 150 feet horizontally as shown below. 88 ft 6 ft 0 150 1) What is the amplitude of the function? 2) What is the midline/vertical shift of the function? [Hint: (highest point + lowest point)/2] 3) What is its period? 4) What is the phase shift for a cosine function? 5) What is the phase shift for a sine function? 6) What is the cosine equation for this function? 7) What is the sine equation for this function? 150 75 :: 42 #300 #41 150 ft to the right :: 225 ft to the right 42 44 300 ft to the right :: 0 ft to the right :: y = 44 cos(x) + 47 :: y = 41 cos(x) + 47 :: y = 41 cos(x) + 47 :: y = 41 sin ( - 225) + 47 y = 41 sin(x - 300) + 47 y = 41 sin :: 250 ft to the right :: 1 ft to the right #47 #91 y = 44 cos(x) + 41 :: y = 44 sin (225) + 41 :: y = 44 sin 150(150) + 47 (300) + 47
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