would would this equation look like? is it a circle?
r=4sin3(theta)
To determine if the equation r = 4sin(3θ) represents a circle, we'll first need to understand the polar coordinate system.
In the polar coordinate system, a point (r, θ) represents the radius (r) and angle (θ) from the origin to that point. In this system, r can take any positive value, while θ is usually given in radians and can range from 0 to 2π (or 0 to 360 degrees).
To visually analyze the equation r = 4sin(3θ), we can plot some points by substituting various values for θ into the equation. Let's use a table of values to calculate a few points:
θ | r = 4sin(3θ)
----------------------
0 | 0
π/6 | 2
π/3 | 4
π/2 | 0
2π/3 | -4
5π/6 | -2
π | 0
By plotting these points on a polar coordinate system, we can observe the shape of the graph. After plotting all the points, we see that the shape is a flower-like curve with six petals, which is commonly known as a rose curve or a rhodonea curve.
Therefore, the equation r = 4sin(3θ) does not represent a circle. It represents a rose curve with six petals.