Evaluate Without Using a Calculator $\sin \theta$ , If $\cos \theta = \frac { 4 } { 7 }$

Multiple Choice

Evaluate without using a calculator.
- $\sin \theta$ , if $\cos \theta = \frac { 4 } { 7 }$ and $\tan \theta < 0$

A) $- \frac { \sqrt { 33 } } { 4 }$
B) $- \frac { \sqrt { 33 } } { 7 }$
C) $- \sqrt { 33 }$
D) $- \frac { 7 } { 4 }$