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) $\sin ( 2 \theta + 1.0122 )$

Question

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) $\sin ( 2 \theta + 1.0122 )$

Quizplus · Accepted Answer

The Answer of 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) $\sin ( 2 \theta + 1.0122 )$

Use the Formula asin⁡Bθ+bcos⁡Bθ=a2+b2sin⁡(Bθ+C)a \sin B \theta + b \cos B \theta = \sqrt { a ^ { 2 } + b ^ { 2 } } \sin ( B \theta + C )asinBθ+bcosBθ=a2+b2​sin(Bθ+C)

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