Use the Half-Angle Formulas to Determine the Exact Value of the Following

question 65

Multiple Choice

Use the half-angle formulas to determine the exact value of the following.
$\cos \left( 22.5 ^ { \circ } \right)$

• A) \(- \frac { \sqrt { 2 + \sqrt { 3 } } } { 2 }\)
• B) \(\frac { \sqrt { 2 - \sqrt { 2 } } } { 2 }\)
• C) \(- \frac { \sqrt { 2 - \sqrt { 2 } } } { 2 }\)
• D) \(\frac { \sqrt { 3 - \sqrt { 3 } } } { 2 }\)
• E) \(\frac { \sqrt { 2 + \sqrt { 2 } } } { 2 }\)

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Definitions:

Mesmer

An 18th-century physician known for developing a theory of animal magnetism and for his contribution to the field we now call hypnotism.

Mental Illness

Encompasses a wide range of mental health conditions that affect mood, thinking, and behavior, leading to distress or difficulty functioning.

Psychological Abnormality

A behavioral, emotional, or cognitive dysfunction that is unusual for the cultural context, causes distress or impairment, and is not expected as part of normal development.

Somatogenic

Pertains to physical causes of psychological symptoms, originating from bodily or biological factors.