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

question 54

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)
• \(\frac { \partial ( x , y ) } { \partial ( \alpha , \beta ) } = - \alpha\)

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