Calculate the next pair of inequalities for sin x and cos x by integrating the results of

Question:

Calculate the next pair of inequalities for sin x and cos x by integrating the results of Exercise 53. Can you guess the general pattern?

Data From Exercise 53

Evaluate the integral in terms of the constants.

1 X - - x 2 +3 6 cos x 1- - sin x x - 2 + 24 x3 x-5 + 6 120 (for x 0)

Verify these inequalities for x = 0.1. Why have we specified x ≥ 0 for sin x but not for cos x?

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Nov 26, 2023 03:24 AM

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Calculate the next pair of inequalities for sin x and cos x by integrating the results of

Question:

1 X - - x² 2 +3 6 cos x ≤ 1- - sin x ≤ x - 2 + 24 x3 x-5 + 6 120 (for x ≥ 0)

Step by Step Answer:

Integrating over the interval 0 x yields Solving for cos x and yields 13 ...View the full answer

Calculus

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