ANSWER
It is not symmetrical to the polar axis
EXPLANATION
To show that the curve
[tex]\text{ To show that the curve r = 3 + 3 sin }\theta\text{ is symmetrical to the polar axis, replace }\theta\text{ by -}\theta[/tex][tex]if\text{ r \lparen}\theta)\text{ = r \lparen-}\theta),\text{ then, the curve is symmetrical, otherwise it is not symmetrical}[/tex][tex]\begin{gathered} r(\theta)\text{ = 3 + 3 sin }\theta \\ r(-\theta)\text{ = 3 + 3sin\lparen-}\theta) \\ Since\text{ sine is an odd function, sin\lparen-}\theta)\text{ = - sin }\theta \\ r(-\theta)\text{ = 3 - 3sin }\theta \\ Since\text{ r\lparen}\theta)\ne\text{ r\lparen-}\theta),\text{ the curve r = 3 + 3 sin }\theta\text{ is not symmetrical to the polar axis} \end{gathered}[/tex]
