Use the Trigonometric Substitution to Rewrite the Algebraic Expression as a Trigonometric

question 58

Multiple Choice

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of $\theta$ , where $- \frac { \pi } { 2 } < x < \frac { \pi } { 2 }$ .Then find sin $\theta$ and cos $\theta$ . $4 = \sqrt { 16 - x ^ { 2 } } , x = 4 \sin \theta$

• A) \(16 \cos \theta = 4 ; \sin \theta = 0 ; \cos \theta = 1\)
• B) \(4 \cos \theta = 4 ; \sin \theta = 0 ; \cos \theta = 1\)
• C) \(16 \sin \theta = 4 ; \sin \theta = 0 ; \cos \theta = 1\)
• D) \(4 \cos \theta = 4 ; \sin \theta = 1 ; \cos \theta = 0\)
• E) \(4 \sin \theta = 4 ; \sin \theta = 0 ; \cos \theta = 1\)

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Definitions:

Multiple Relationships

Situations in which a professional or therapist has more than one type of relationship with a client or patient, raising concerns about conflict of interest and ethics.

Power Differential

The difference in power or authority between two individuals or groups, often impacting interactions and outcomes.

Managing Boundaries

The practice of establishing and maintaining clear limits in professional and personal relationships.

Helping Relationship

A professional and supportive relationship between a helper (e.g., therapist, counselor) and a client, focused on the client’s needs, growth, and well-being.