What is the shape graphed by the function r = 1+ sin theta

Is known as a "heart" shape.

Step-by-step explanation:

r = 1 + sin(θ)

Let's do it without a graph, let's use only math and logic:

remember that θ is measured from the x-axis

when θ = 0, we have r = 1 (so we have a radius of 1 over the x-axis)

when θ = pi/2, we have r = 1 + sin(pi/2) = 2

when θ = pi, we have r = 1 + sin(pi) = 1

when θ = 3*pi/2, we have r = 1 + sin(3*pi/2) = 0

First, we have symetry around the y-axis,

now, notice that the value of x in θ = 0, θ = pi and θ = 3*pi/2 is the same. so this is not a circle, this is actually a circle where the bottom part is flatted.

But not actually flat, because between θ = pi and θ = 2pi we are in the negative y-axis, so in this region we have two small bumps that connect in the point (0, 0)

This is a kinda "heart" shape.

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step-by-step explanation:

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