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

question 238

Multiple Choice

Use the formula $a \sin B \theta + b \cos B \theta = \sqrt { a ^ { 2 } + b ^ { 2 } } \sin ( B \theta + C )$ , where $C = \arctan ( b / a ) , a = 1 , b = 3 , B = 2$ , 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) \(\sqrt { 10 }\) \(\sin ( 2 \theta + 1.249 )\)
• B) \(\sqrt { 10 }\) \(\sin ( \theta - 1.249 )\)
• C) \(\sqrt { 10 }\) \(\sin ( 2 \theta - 1.249 )\)
• D) \(\sqrt { 10 }\) \(\sin ( \theta + 1.249 )\)
• E) \(\sin ( 2 \theta + 1.249 )\)

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