Make table of values for r = -2sinθ

Question

This is for polar graphing project

Answer 1

If r = -2sinθ, then r² = -2rsinθ.

So, x² + y² = -2y

x² + (y²+2y) = 0

Complete the square to obtain x² + (y²+2y+1) = 1

So, (x-0)² + (y+1)² = 1. This is a circle centered at (0,-1) with radius 1 traced out clockwise as θ increases from 0 to 2π. .

Table of values:

r 0 -2 0 2 0

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θ 0 π/2 π 3π/2 2π