Question

Choose the point that shows the correct location for the polar coordinate (3,(2π)/3)

Answer 1

The point that shows the correct location for the polar coordinate
`$(3, (2 \pi)/(3))$` is **point D**.

Here's how to find it:

1. **Remember the relationship between polar and rectangular coordinates:** In a polar coordinate system, a point is represented by its distance from the origin (r) and the angle it makes with the positive x-axis (θ). We can convert between polar and rectangular coordinates using the following formulas:

x = r cos(θ)

y = r sin(θ)

2. **Plug in the given values:** In this case, r = 3 and θ =
`(2 \pi)/(3).`Therefore:

x = 3 cos
`((2 \pi)/(3)) = 3 * (-0.5) = -1.5`

y = 3 sin
`((2 \pi)/(3)) = 3 * ((√(3))/(2)) = (3 √(3))/(2)`

3. **Plot the point:** Based on the calculations, the point should be plotted at
`(-1.5, (3 √(3))/(2))`. Looking at the provided image, this corresponds to **point D**.

Therefore, **point D** is the correct location for the polar coordinate
`$(3, (2 \pi)/(3))$`

Answer 2

It is point A.

From the polar graph, we trace 3 on the horizontal axis and go from there round to where the point intersects the 2π/3 line and this is precisely at point A. It is worthy to note that 2π/3 = 120 degrees.