(a) Explanation Given Information: The provided pair of functions is f ( t ) = cos t ; g ( t ) = − 2.5 cos ( t ) . Graph: Consider the function f ( t ) = cos t . Compare the function with general expression of cosine function: f ( x ) = A cos [ ω ( x − β ) ] + C . Here, A = 1 , which define the distance of oscillations up and down that is ± A . The sine function f ( t ) = cos t oscillates between − 1 , and 1 . The vertical offset which is the height of the baseline is C = 0 . The angular frequency which is the number of cycles in every interval of length 2 π is ω = 1 . The period or wavelength which is the length of each cycle is, P = 2 π 1 = 2 π The phase shift which is the distance to which the function is shifted horizontally is β = 0 . Consider the function g ( t ) = − 2.5 cos ( t ) . Compare the function with general expression of cosine function: f ( x ) = A cos [ ω ( x − β ) ] + C (b) To determine To graph: The sketch of the pair of functions f ( t ) = cos t ; g ( t ) = − 2.5 cos ( t ) on the same set of axes using technology.

7th Edition

ISBN: 9781337514309

Author: Waner

Publisher: Cengage

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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Chapter 9.1, Problem 11E

(a)

To determine

To graph: The sketch of the pair of functions f(t)=cost;g(t)=−2.5cos(t) on the same set of axes without any technological help.

(b)

To determine

To graph: The sketch of the pair of functions f(t)=cost;g(t)=−2.5cos(t) on the same set of axes using technology.

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Chapter 9.1, Problem 10E

Chapter 9.1, Problem 12E

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Chapter 9 Solutions

Applied Calculus

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To graph: The sketch of the pair of functions f ( t ) = cos t ; g ( t ) = − 2.5 cos ( t ) on the same set of axes without any technological help.

Solution Summary: The author illustrates the graph of the pair of functions f(t)=mathrmcost; and compares it with the general expression of cosine function.