Explanation Given Information: The provided curve is: Formula Used: The value of Amplitude in the cosine function is the height of peak above the baseline and named it as A. Then the vertical offset is the height of the baseline and it is named as C . The angular frequency is the number of cycles in every interval of length 2 π denoted by ω . The period or wavelength is the length of each cycle which is given by P = 2 π ω . Then β which is the phase shift. The cosine function is given by f ( x ) = A cos [ ω ( x − β ) ] + C . Calculation: Consider the provided curve. Determine the value of Amplitude which is the height of peak above the baseline. A = 3 Then determine the vertical offset which is the height of the baseline. C = h − A Where h is the total height of the peak and A is Amplitude. C = − 5 + 3 C = − 2 Then determine the period or wavelength which is the length of each cycle. P = 0.5 Then determine the angular frequency which is the number of cycles in every interval of length 2 π . ω = 2 π P ω = 2 π 0.5 ω = 4 π Then determine the phase shift which is the distance to which the function is shifted horizontally. If α = 0.25 then, β = α + P 4 β = 0.25 + 0.5 4 β = 0.25 + 0.125 β = 0.375 If α = − 0

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ISBN: 9781337291408

Author: Stefan Waner, Steven Costenoble

Publisher: Brooks Cole

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Chapter 9, Problem 8RE

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Chapter 9, Problem 7RE

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Applied Calculus, Loose-leaf Version

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