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(a) Find the first four terms of the Taylor Series of f(x) = cos about To, writing your answer in its simplest exact form, i.e. without the use of a calculator. (b) Use the first four terms of the series in part (a) to obtain an approximate value of cos (25°). Write your answer first in its exact form, then give your answer to 6 decimal places. (Hint: Use radians). (c) Give the error, to 6 decimal places, between the value of cos (25°) and its Taylor series approximation to four terms, and comment on your answer.

(a) Find the first four terms of the Taylor Series of f(x) = cos about To, writing your answer in its simplest exact form, i.e. without the use of a calculator. (b) Use the first four terms of the series in part (a) to obtain an approximate value of cos (25°). Write your answer first in its exact form, then give your answer to 6 decimal places. (Hint: Use radians). (c) Give the error, to 6 decimal places, between the value of cos (25°) and its Taylor series approximation to four terms, and comment on your answer.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) Find the first four terms of the Taylor Series of f(x) = cos about To, writing your answer in its simplest exact form, i.e. without the use of a calculator. (b) Use the first four terms of the series in part (a) to obtain an approximate value of cos (25°). Write your answer first in its exact form, then give your answer to 6 decimal places. (Hint: Use radians). (c) Give the error, to 6 decimal places, between the value of cos (25°) and its Taylor series approximation to four terms, and comment on your answer.
Transcribed Image Text:(a) Find the first four terms of the Taylor Series of f(x) = cos about To, writing your answer in its simplest exact form, i.e. without the use of a calculator. (b) Use the first four terms of the series in part (a) to obtain an approximate value of cos (25°). Write your answer first in its exact form, then give your answer to 6 decimal places. (Hint: Use radians). (c) Give the error, to 6 decimal places, between the value of cos (25°) and its Taylor series approximation to four terms, and comment on your answer.
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