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 $C = \arctan ( b / a ) , a = 5 , b = 8 , B = 1$ ,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) $\sqrt { 89 }$ $\sin ( \theta + 1.0122 )$
B) $\sqrt { 89 }$ $\sin ( \theta - 1.0122 )$
C) $\sqrt { 89 }$ $\sin ( 2 \theta - 1.0122 )$
D) $\sqrt { 89 }$ $\sin ( 2 \theta + 1.0122 )$
E) $\sin ( 2 \theta + 1.0122 )$

Correct Answer:

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