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

question 12

Multiple Choice

Use the formula $\operatorname { asin } B \theta + b \cos B \theta = \sqrt { a ^ { 2 } + b ^ { 2 } } \sin ( B \theta + C )$ where $\bar { C } = \arctan ( b / a ) , a > 0$ to find the trigonometric expression in the following forms.
$\begin{array} { l } y = \sqrt { a ^ { 2 } + b ^ { 2 } } \sin ( B \theta + C ) \\2 \sin \theta + 7 \cos \theta\end{array}$

• A) \(\sqrt { 53 } \sin ( \theta + 1.2925 )\)
• B) \(\sqrt { 53 } \sin ( \theta - 1.2925 )\)
• C) \(2 \sin ( \theta + 1.2925 )\)
• D) \(7 \sin ( \theta + 1.2925 )\)
• E) \(\sin ( \theta + 1.2925 )\)

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Definitions:

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An effort to explain how the existence of evil is compatible with the existence of God.

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A German-American theologian and philosopher known for his works on existentialist philosophy and Christian existentialism, notably "The Courage to Be."

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