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

question 23

Multiple Choice

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

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

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Definitions:

Deferred Annuity

A financial product that delays payments of income, installments, or a series of payments until a specified future date.

Ordinary Annuity

A sequence of identical disbursements done at consecutive period ends over a predefined duration.

Perpetuity

A type of annuity that generates an infinite series of future payments, theoretically lasting forever.

Compounded Quarterly

The process of calculating interest on both the initial principal and the accumulated interest over previous quarters, increasing the total amount at a quarterly rate.