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

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) $6 \sqrt { 10 }$ $\sin ( \theta + 0.3218 )$

Correct Answer:

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