The Linear Approximation $L ( x )$ To $f ( x ) = \sin x$

Multiple Choice

The linear approximation $L ( x )$ to $f ( x ) = \sin x$ near $x _ { 0 } = - \frac { \pi } { 6 }$ is

A) $- \frac { 1 } { 2 } - \frac { \sqrt { 3 } } { 2 } \left( x + \frac { \pi } { 6 } \right)$
B) $- \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } \left( x + \frac { \pi } { 6 } \right)$
C) $- \frac { \sqrt { 3 } } { 2 } + \frac { 1 } { 2 } \left( x + \frac { \pi } { 6 } \right)$
D) $- \frac { \sqrt { 3 } } { 2 } - \frac { 1 } { 2 } \left( x + \frac { \pi } { 6 } \right)$
E) $- \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } \left( x - \frac { \pi } { 6 } \right)$