Explanation Formula used: Maclaurin expansion of cos x : “The Maclaurin expansion of cos x is given by, cos x = 1 − x 2 2 ! + x 4 4 ! − x 6 6 ! + ⋯ ” Calculation: Obtain the Maclaurin expansion of cos 2 x by replacing x by 2 x in the Maclaurin expansion of cos x as shown below. cos 2 x = 1 − ( 2 x ) 2 2 ! + ( 2 x ) 4 4 ! − ( 2 x ) 6 6 ! + ⋯ = 1 − 4 x 2 2 + 16 x 4 24 − 64 x 6 720 + ⋯ = 1 − 2 x 2 + 2 3 x 4 − 4 45 x 6 + ⋯ Now obtain the first four terms of expansion for sin 2 x by using the identity sin 2 x = 1 2 ( 1 − cos 2 x ) as follows

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780134434636

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 30, Problem 57RE

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The first four terms of expansion for sin2x by using the identity sin2x=12(1−cos2x) and cosx.

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Chapter 30, Problem 56RE

Chapter 30, Problem 58RE

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Chapter 30 Solutions

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

Ch. 30.1 - Prob. 1PE Ch. 30.1 - Prob. 2PE Ch. 30.1 - Prob. 1E Ch. 30.1 - Prob. 2E Ch. 30.1 - Prob. 3E Ch. 30.1 - Prob. 4E Ch. 30.1 - Prob. 5E Ch. 30.1 - Prob. 6E Ch. 30.1 - Prob. 7E Ch. 30.1 - Prob. 8E

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The first four terms of expansion for sin 2 x by using the identity sin 2 x = 1 2 ( 1 − cos 2 x ) and cos x .

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The first four terms of expansion for sin2x by using the identity sin2x=12(1−cos2x) and cosx.

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Chapter 30 Solutions