Find the Jacobian of the Transformation $$x = 5 \alpha \sin \beta , y = 4 \alpha \cos \beta$$

question 25

Multiple Choice

Find the Jacobian of the transformation. $$x = 5 \alpha \sin \beta , y = 4 \alpha \cos \beta$$

• A) \(\frac { \partial ( x , y ) } { \partial ( \alpha , \beta ) } = 9 \alpha\)
• B) \(\frac { \partial ( x , y ) } { \partial ( \alpha , \beta ) } = 36 \alpha\)
• C) \(\frac { \partial ( x , y ) } { \partial ( \alpha , \beta ) } = - 20 \alpha\)
• D) \(\frac { \partial ( x , y ) } { \partial ( \alpha , \beta ) } = - 20 \alpha \sin \beta \cos \beta\)
• E) \(\frac { \partial ( x , y ) } { \partial ( \alpha , \beta ) } = - \alpha\)

---

Definitions:

Diverse Clients

Refers to a broad spectrum of clients from different backgrounds, cultures, ethnicities, and personal experiences in a therapeutic setting.

Strengths

The inherent capabilities, skills, and positive attributes that an individual or group possesses, which can be leveraged for personal growth or achieving goals.

Weaknesses

Aspects of an individual's character or skills that are less developed or present challenges in one's personal or professional life.

Analytical Psychology

A branch of psychology founded by Carl Jung that focuses on exploring the unconscious and its influence on the individual.