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) \(\sin ( 2 \theta + 1.249 )\)

---

Definitions:

Marginal Revenue

The additional income from selling one more unit of a good; sometimes equal to the price of the good.

Total Fixed Costs

The sum of all costs that remain constant regardless of the level of production or output in a business.

Recession

A period of declining real GDP, accompanied by lower real income and higher unemployment.

Average Fixed Cost

The fixed expenses of a business spread out over the total number of units produced, decreasing as production increases.