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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 74E

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Question

(a) Find the Maclaurin polynomials of orders 2, 3 and 4 for f(x) = cos(x).
(b) Use the result obtained in part (a) to approximate cos 10° with a quadratic polynomial, p2, and
compare this approximation to the result from your calculator or from Google.
Remember to convert from degrees to radians before using the Maclaurin polynomial.
(c) Use Taylor's Theorem with the Lagrange form of the remainder to show that
| cos r – p2(x)| <
4!
How does this compare with the accuracy that you found in part (b)?
(d) Find the MacLaurin series for f(x) = cos(x) and write it using sigma notation.
(e) Differentiate the MacLaurin series for g(x) = sin(x) term by term and confirm that you obtain the
MacLaurin series for the derivative of sin(x).

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