Question

Suppose a point has polar coordinates -4. 4x 3 *). with the angle measured in radians. Find two additional polar representations of the point. write each coordinate in simplest form with the angle in (-21, 21).

Answer 1

The given point with polar coordinates (-4, 4 * 3) can also be represented as (4, 4 * 3 - π) or (4, 4 * 3 + 2π) within the range (-2π, 2π). This is due to the periodic nature of trigonometric functions in the polar coordinate system.

Step-by-step explanation:

Solution:

In the polar coordinate system, a point can be represented with different coordinates. Given the polar coordinate (-4, 4 * 3), we can find additional polar representations.

A point in polar can be represented as (r, θ) and (-r, θ+π), where
r is the radial coordinate (non-negative real number) and θ is the angular coordinate.

So, a given point (-4, 4 * 3) can be shifted by adding 2π to the angle 4*3. The angle will remain in the range (-2π, 2π).

Thus, the point can also be represented as: