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 $C = \arctan ( b / a ) , a = 1 , b = 3 , B = 2$ , 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) $\sqrt { 10 }$ $\sin ( 2 \theta + 1.249 )$
B) $\sqrt { 10 }$ $\sin ( \theta - 1.249 )$
C) $\sqrt { 10 }$ $\sin ( 2 \theta - 1.249 )$
D) $\sqrt { 10 }$ $\sin ( \theta + 1.249 )$
E) $\sin ( 2 \theta + 1.249 )$