Using the first three nonzero terms of the Maclaurin series of cos x, the approximated value of cos1 is

A) $\frac { 13 } { 24 }$
B) $\frac { 100 } { 161 }$
C) $\frac { 101 } { 120 }$
D) $\frac { 13 } { 15 }$
E) $\frac { 8 } { 3 }$

Question

Using the first three nonzero terms of the Maclaurin series of cos x, the approximated value of cos1 is

A) $\frac { 13 } { 24 }$
B) $\frac { 100 } { 161 }$
C) $\frac { 101 } { 120 }$
D) $\frac { 13 } { 15 }$
E) $\frac { 8 } { 3 }$

Quizplus · Accepted Answer

The first three nonzero terms of the Maclaurin series of cos x are:$$cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!}$$Substituting x = 1, we get:$$cos 1 = 1 - \frac{1^2}{2!} + \frac{1^4}{4!} = 1 - \frac{1}{2} + \frac{1}{24} = \frac{13}{24}$$

Using the First Three Nonzero Terms of the Maclaurin Series 1324\frac { 13 } { 24 }2413​

Using the First Three Nonzero Terms of the Maclaurin Series $\frac { 13 } { 24 }$