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

Is the curve r = 3 + 3sin θ symmetrical to the polar axis? Justify your answer algebraically-example-1
User DNF
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1 Answer

15 votes
15 votes

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}

User Steg Verner
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