Question

Is the curve r = 3 + 3sin θ symmetrical to the polar axis? Justify your answer algebraically.

Answer 1

ANSWER

It is not symmetrical to the polar axis

Step-by-step explanation

To show that the curve

`\text{ To show that the curve r = 3 + 3 sin }\theta\text{ is symmetrical to the polar axis, replace }\theta\text{ by -}\theta`
`if\text{ r \lparen}\theta)\text{ = r \lparen-}\theta),\text{ then, the curve is symmetrical, otherwise it is not symmetrical}`
`\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)\\e\text{ r\lparen-}\theta),\text{ the curve r = 3 + 3 sin }\theta\text{ is not symmetrical to the polar axis} \end{gathered}`