Solve the Problem $x = 3 \sin t , y = \cos t , - \frac { \pi } { 2 } \leq t \leq \frac { \pi } { 2 }$

question 35

Multiple Choice

Solve the problem.
-Find the point on the curve $x = 3 \sin t , y = \cos t , - \frac { \pi } { 2 } \leq t \leq \frac { \pi } { 2 }$ , closest to the point $\left( \frac { 4 } { 3 } , 0 \right)$ . (Hint: Minimize the square of the distance as a function of $t$ .)

• A) \(\left( \frac { 3 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)\)
• B) \(( - 3,0 )\)
• C) \(\left( \frac { \sqrt { 3 } } { 2 } , \frac { 3 } { 2 } \right)\)
• D) \(( 3,0 )\)

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