Problem

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

Solution

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

From Solvely APP
Source: https://solvelyapp.com/problems/13723/

Get free Solvely APP to solve your own problems!

solvely Solvely
Download