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

Use the formula $a \sin B \theta + b \cos B \theta = \sqrt { a ^ { 2 } + b ^ { 2 } } \cos ( B \theta - C )$ ,where $C = \arctan ( a / b ) , a = 13 , b = 6 , B = 3$ to rewrite the trigonometric expression in the following form.​ $y = \sqrt { a ^ { 2 } + b ^ { 2 } } \cos ( B \theta - C )$ ​ $a \sin B \theta + b \cos B \theta$ ​

A) 6 $\cos ( 3 \theta - 1.1384 )$
B) $\sqrt { 205 }$ $\cos ( 3 \theta + 1.1384 )$
C) $\sqrt { 205 }$ $\cos ( 3 \theta - 1.1384 )$
D) 13 $\cos ( 3 \theta + 1.1384 )$
E) 13 $\cos ( 3 \theta - 1.1384 )$

Correct Answer:

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