CPM Homework Help : CALC Problem 12-82

Multiple Choice: Which of the following is the slope of the tangent to the polar curve $r ( \theta ) = \frac { 1 } { 1 + \operatorname { sin } \theta }$ at the point $( r , \theta ) = ( \frac { \pi } { 6 } , \frac { 2 } { 3 } )$ ?

$- \frac { \sqrt { 3 } } { 3 }$

$- \frac { 2 \sqrt { 3 } } { 9 }$

$- \frac { \pi } { 3 }$

$\frac { 2 \sqrt { 3 } } { 3 }$

$\frac { \sqrt { 3 } } { 3 }$

Hint:

Remember, the slope is $dy/dx$ , so you will need equations for $x$ and $y$ .

Step:

Now repeat this process for $x$ .