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

question 32

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) \(\frac { \sqrt { 2 + \sqrt { 2 } } } { 2 }\)

---

Definitions:

Variable-interval

An unpredictable reinforcement schedule that provides rewards after an unspecified time period following a response.

Intermittent Reinforcement

Intermittent Reinforcement is a conditioning schedule in which rewards or consequences are given only some of the time, creating strong and persistent responses.

Continuous Reinforcement

A learning process in which a behavior is reinforced each time it is exhibited, leading to a faster acquisition of the behavior.

Immediate Reinforcement

The prompt delivery of a reward or punishment following a behavior, which increases the likelihood of that behavior's recurrence.