Use the Formula $a \sin B \theta + b \cos B \theta = \sqrt { a ^ { 2 } + b ^ { 2 } } \sin ( B \theta + C )$

Multiple Choice

Use the formula $a \sin B \theta + b \cos B \theta = \sqrt { a ^ { 2 } + b ^ { 2 } } \sin ( B \theta + C )$ , where $C = \arctan ( b / a ) , a = 18 , b = 6 , B = 3$ , to rewrite the trigonometric expression in the following form.
$y = \sqrt { a ^ { 2 } + b ^ { 2 } } \sin ( B \theta + C )$ $a \sin B \theta + b \cos B \theta$

A) $6 \sqrt { 10 }$ $\sin ( \theta - 0.3218 )$
B) $6 \sqrt { 10 }$ $\sin ( 3 \theta + 0.3218 )$
C) $\sin ( 3 \theta + 0.3218 )$
D) $6 \sqrt { 10 }$ $\sin ( 3 \theta - 0.3218 )$
E) $6 \sqrt { 10 }$ $\sin ( \theta + 0.3218 )$