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$(5$ points$)$ The second, eighth, and last ones are wrong

Sketch the curve given in polar coordinates by the equation $r=7+\frac{13}{2}sin().$

$($a$)$ For each value of $$ given in the tables below fill in the corresponding $r-$value for which the point $(r,)$ satisfies this equation.

Note: For the purposes of sketching we will use $0\mathrm{.}9$ for $\frac{\sqrt[\phantom{2}]{3}}{2}$ and $0\mathrm{.}7$ for $\frac{\sqrt[\phantom{2}]{2}}{2}.$

$\backslash$table$[[=,-\frac{}{2},-\frac{}{3},-\frac{}{4},-\frac{}{6}$