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Approximating a Function Value using a Taylor Polynomial

APCALC-5VGK7J

What is the approximate value of $\sin\left( \frac { 1 }{ 2 } \right) $ obtained by using a fourth-degree Taylor polynomial for $\sin\left( x \right) $ about $x=0$?

A

$1-\cfrac { 1 }{ 8 } +\cfrac { 1 }{ 384 } $

B

$\cfrac { 1 }{ 2 } -\cfrac { 1 }{ 48 } $

C

$\cfrac { 1 }{ 2 } -\cfrac { 1 }{ 8 } $

D

$1-\cfrac { 1 }{ 2 } -\cfrac { 1 }{ 24 } $