Problem

Which type of symmetry does $r=2 \sin \theta \quad$ have?

Answer

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Answer

\(\boxed{\text{The given equation } r=2 \sin \theta \text{ has symmetry about the x-axis}}\)

Steps

Step 1 ：The given equation is in polar coordinates, which is of the form $r = a \sin \theta$ or $r = a \cos \theta$ representing a circle with radius $a/2$ centered at $(0, a/2)$ or $(0, -a/2)$ respectively.

Step 2 ：The equation $r = 2 \sin \theta$ represents a circle with radius 1 centered at $(0, 1)$.

Step 3 ：This circle has symmetry about the x-axis (or in polar coordinates, symmetry about the horizontal line $\theta = \pi/2$).

Step 4 ：\(\boxed{\text{The given equation } r=2 \sin \theta \text{ has symmetry about the x-axis}}\)

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