Determine All Solutions of the Equation in Radians $\sin \frac { \theta } { 2 }$

question 254

Multiple Choice

Determine all solutions of the equation in radians.
-Find $\sin \frac { \theta } { 2 }$ , given that $\cos \theta = \frac { 1 } { 4 }$ and $\theta$ terminates in $0 < \theta < 90 ^ { \circ }$ .

• A) \(\frac { \sqrt { 8 - 2 \sqrt { 15 } } } { 4 }\)
• B) \(\frac { \sqrt { 10 } } { 4 }\)
• C) \(\frac { \sqrt { 8 + 2 \sqrt { 15 } } } { 4 }\)
• D) \(\frac { \sqrt { 6 } } { 4 }\)

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Definitions:

Panic Disorder

An anxiety disorder that consists of sudden, overwhelming attacks of terror.

Generalized Anxiety Disorder

An anxiety disorder with a state of constant anxiety not associated with any specific object or event.

Overpowering Terror

An intense, extreme fear that overwhelms and paralyzes an individual, often without a clear or immediate external threat.

Panic Attacks

Sudden episodes of intense fear or anxiety that may include physical symptoms such as palpitations, sweating, or chest pain.