Question

Plot the point that has the given polar coordinates. (−2,−4π​) Give two other polar coordinate representations of the point, one with r<0 and one with r>0. (r,θ)=(()(r,θ)​)( smaller r-value )×​

Answer 1

To plot the point with polar coordinates (-2, -4π), we convert it to Cartesian coordinates. The point is (-2, 0). Other polar coordinate representations are (-2, 0) for r < 0 and (2, -4π) for r > 0.

Step-by-step explanation:

To plot a point with given polar coordinates (-2, -4π), we need to convert it to Cartesian coordinates.

The Cartesian coordinates can be found using the formulas:

x = r * cosθ and y = r * sinθ

Plugging in the values, we get:

x = -2 * cos(-4π) and y = -2 * sin(-4π)

Simplifying the equations, we find that x = -2 and y = 0.

So, the point with the given polar coordinates is (-2, 0).

For two other polar coordinate representations, we can consider r with a negative value and a positive value:

The point with r < 0 can be represented as (-|-2|, -4π), which is (-2, 0)

The point with r > 0 can be represented as (|-2|, -4π), which is (2, -4π)

Answer 2

To plot the point with the given polar coordinates (−2,−4π​), convert them to Cartesian coordinates using the formulas x = r * cos(θ) and y = r * sin(θ). The point is (-2, 0) in Cartesian coordinates. Two other polar coordinate representations of the point are (2, π​) and (-2, π​).

Step-by-step explanation:

To plot the point with the given polar coordinates (−2,−4π​), we can use the formula:

x = r * cos(θ)

y = r * sin(θ)

Substituting the values, we get:

x = -2 * cos(-4π​)

y = -2 * sin(-4π​)

Simplifying further, we get:

x = -2

y = 0

So, the point is (-2, 0) in Cartesian coordinates.

For two other polar coordinate representations, one with r<0 would be (2, π​), and one with r>0 would be (-2, π​).