Question

Write two polar representation for the plotted point if -pi<0<=pi. Positive r(2,0), negative r is (-2,?)

what is the question mark

Answer 1

The equivalent negative radial coordinate for the point with positive polar representation (2,0) is (-2, π). The negative radial coordinate changes the direction by adding π to the angle.

Step-by-step explanation:

The question pertains to finding a polar representation for a point with a negative radial coordinate given its positive counterpart.

In polar coordinates, a point can be represented in two ways: (r, θ) or (-r, θ+ π), where r is the radial distance from the origin to the point and θ is the angle from the positive x-axis to the line connecting the origin to the point.

Given the positive polar representation of a point is (2,0), we can find the negative r representation by adding π to the angle component, converting (2,0) to (-2, π).

In general, for any positive polar coordinate (r, θ), the equivalent negative r representation can be found by using (-r, θ + π).

In your specific case, the point with positive polar coordinates (2, 0) will have equivalent negative polar coordinates of (-2, π).

Therefore, the question mark in the negative r representation (-2,?) is π.