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

question 24

Multiple Choice

Use the formula $a \sin B \theta + b \cos B \theta = \sqrt { a ^ { 2 } + b ^ { 2 } } \cos ( B \theta - C )$ ,where $C = \arctan ( a / b ) , a = 13 , b = 6 , B = 3$ to rewrite the trigonometric expression in the following form.​ $y = \sqrt { a ^ { 2 } + b ^ { 2 } } \cos ( B \theta - C )$ ​ $a \sin B \theta + b \cos B \theta$ ​

• A)6 \(\cos ( 3 \theta - 1.1384 )\)
• B) \(\sqrt { 205 }\) \(\cos ( 3 \theta + 1.1384 )\)
• C) \(\sqrt { 205 }\) \(\cos ( 3 \theta - 1.1384 )\)
• D)13 \(\cos ( 3 \theta + 1.1384 )\)
• E)13 \(\cos ( 3 \theta - 1.1384 )\)

Appreciate the significance of cognitive research findings in real-world applications, such as risk assessment and problem-solving.

Analyze the effects of stereotyping and bias on perception and behavior.

Recognize the role of sudden insight and its neurobiological basis in problem-solving.

Understand the distinction between and applications of algorithms and heuristics in solving complex problems.

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Definitions:

Trachea

The windpipe, a tube extending from the larynx towards the lungs, providing the passage of air to the respiratory system.

Larynx

The part of the respiratory tract located in the neck that houses the vocal cords and is involved in breathing, speech, and swallowing.

Conchae

Curved bones in the nasal cavity that help to filter, warm, and moisten the air before it enters the lungs.

Tracheotomy

A surgically made opening in the trachea through which a person will breathe.