Final answer:
The equation represents a parabola with an eccentricity of 1.
Step-by-step explanation:
To find the eccentricity and identify the conic, let's first rearrange the equation using the trigonometric identity sin^2(θ) + cos^2(θ) = 1:
r = 6/2 + sin(θ)
r = 3 + sin(θ)
Now, we can see that the equation has the general form for a parabola, x = ay^2 + by + c. Therefore, the conic represented by the equation is a parabola.
The eccentricity can be defined as the square root of 1 plus the coefficient of the squared term divided by the coefficient of the linear term: e = sqrt(1 + 0/1) = sqrt(1) = 1. So, the eccentricity of the conic is 1.