Explanation Given: The given expression is f ( t ) = 10 cos ( t − π 6 ) . Formula used: The formula for the Laplace transform of sin k t and cos k t are L { sin k t } = k s 2 + k 2 and L { cos k t } = s s 2 + k 2 . The trigonometric expression of multiple angles is cos ( a − b ) = cos a cos b + sin a sin b . Calculation: Use the above formula to write the Laplace transform of the given function. L { f ( t ) } = L { 10 cos ( t − π 6 ) } = 10 [ L { cos t cos π 6 + sin t sin π 6 } ] = 10 [ ( cos π 6 ) s s 2 + 1 2 + ( sin π 6 ) 1 s 2 + 1

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 4.1, Problem 40E

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The expression for the Laplace transform of the given function.

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Chapter 4.1, Problem 39E

Chapter 4.1, Problem 41E

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The expression for the Laplace transform of the given function.

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Chapter 4 Solutions