9. Polar Equations

Graphing Other Common Polar Equations

9. Polar Equations

Graphing Other Common Polar Equations

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Multiple Choice

Identify whether the given equation is that of a cardioid, limaçon, rose, or lemniscate.
$r=4\sin2\theta$

Cardioid

Limacon

Rose

Lemniscate

Verified step by step guidance

Recognize the general form of the given polar equation: $ r = 4 \sin 2\theta $. This equation is in the form $ r = a \sin(n\theta) $ or $ r = a \cos(n\theta) $.

Identify the value of $ n $ in the equation. Here, $ n = 2 $.

Recall that when $ n $ is an integer greater than 1, the equation $ r = a \sin(n\theta) $ or $ r = a \cos(n\theta) $ represents a rose curve.

Understand that the number of petals in a rose curve is determined by $ n $. If $ n $ is even, the rose will have $ 2n $ petals. If $ n $ is odd, it will have $ n $ petals.

Since $ n = 2 $ is even, the rose curve described by $ r = 4 \sin 2\theta $ will have $ 2 \times 2 = 4 $ petals, confirming it is a rose.

3:47m

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Graphing Other Common Polar Equations practice set

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Struggling with Trigonometry?

Identify whether the given equation is that of a cardioid, limaçon, rose, or lemniscate.r=4sin2θr=4\sin2\thetar=4sin2θ

Watch next

Graphing Other Common Polar Equations practice set

Identify whether the given equation is that of a cardioid, limaçon, rose, or lemniscate.
$r=4\sin2\theta$