The polar coordinates of a point can be expressed in many ways. The polar coordinates are usually given as (r, θ), where r is the distance from the origin (or the pole) and θ is the angle from the positive x-axis (or polar axis).

Given the rectangular coordinates (-3,0), we can convert these to polar coordinates. The r value is the distance from the origin to the point, which can be calculated using the Pythagorean theorem as sqrt((-3)^2 + 0^2) = 3. The θ value is the angle from the positive x-axis to the point, which in this case is π (or 180 degrees) because the point lies on the negative x-axis.

So the polar coordinates of the point are (3, π). However, we can add any multiple of 2π to the angle and it will still refer to the same point. So (3, π + 2π) or (3, π - 2π) are also valid polar coordinates for the point.

Therefore, the correct answers are:

c. (3, 2π)
e. (3, π)

Question

The polar coordinates of a point can be expressed in many ways. The polar coordinates are usually given as (r, θ), where r is the distance from the origin (or the pole) and θ is the angle from the positive x-axis (or polar axis).

Given the rectangular coordinates (-3,0), we can convert these to polar coordinates. The r value is the distance from the origin to the point, which can be calculated using the Pythagorean theorem as sqrt((-3)^2 + 0^2) = 3. The θ value is the angle from the positive x-axis to the point, which in this case is π (or 180 degrees) because the point lies on the negative x-axis.

So the polar coordinates of the point are (3, π). However, we can add any multiple of 2π to the angle and it will still refer to the same point. So (3, π + 2π) or (3, π - 2π) are also valid polar coordinates for the point.

Therefore, the correct answers are:

c. (3, 2π)
e. (3, π)

Knowee AI · Accepted Answer

The polar coordinates of a point can be expressed in many ways. The polar coordinates are usually given as (r, θ), where r is the distance from the origin (or the pole) and θ is the angle from the positive x-axis (or polar axis).

Given the rectangular coordinates (-3,0), we can convert these to polar coordinates. The r value is the distance from the origin to the point, which can be calculated using the Pythagorean theorem as sqrt((-3)^2 + 0^2) = 3. The θ value is the angle from the positive x-axis to the point, which in this case is π (or 180 degrees) because the point lies on the negative x-axis.

So the polar coordinates of the point are (3, π). However, we can add any multiple of 2π to the angle and it will still refer to the same point. So (3, π + 2π) or (3, π - 2π) are also valid polar coordinates for the point.

Therefore, the correct answers are:

c. (3, 2π)
e. (3, π)

Given the rectangular coordinates, (−3,0)(−3,0) , of a point, select all of the possible polar coordinates of that same point.Question 12Select one or more:a.(−3,2π)(−3,2𝜋)b.(3,−π)(3,−𝜋)c.(3,2π)(3,2𝜋)d.(−3,−π)(−3,−𝜋)e.(3,π)

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