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:

Achievement

The act of accomplishing a task or reaching a goal, often through effort, skill, or courage.

Affiliation

A connection or association with a group or organization.

Social Comparison

A psychological process where individuals evaluate their own abilities and opinions by comparing themselves to others.

Foundation

An underlying basis or principle for something, or an organization established for a specific purpose such as charitable, educational, or research objectives.