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 $C = \arctan ( a / b ) , a = 3 , b = 7 , B = 2$ 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) $\sqrt { 58 }$ $\cos ( 2 \theta + 0.4049 )$
B) $\sqrt { 58 }$ $\cos ( 2 \theta - 0.4049 )$
C) 7 $\cos ( 2 \theta - 0.4049 )$
D) 3 $\cos ( 2 \theta - 0.4049 )$
E) 3 $\cos ( 2 \theta + 0.4049 )$

Correct Answer:

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