Question

Convert the following equations in Cartesian coordinates to an equation in polar coordinates of the form r=f(θ).

Answer 1

To convert equations from Cartesian coordinates to polar coordinates, we can use the relationships: x = r * cos(θ) and y = r * sin(θ). By substituting these equations into the given Cartesian equations, we can express them in polar form.

Step-by-step explanation:

In order to convert equations from Cartesian coordinates to polar coordinates, we need to use the following relationships:

x = r * cos(θ)

y = r * sin(θ)

These equations show the connection between the coordinates (x, y) in the rectangular system and the polar coordinates (r, θ). By substituting these equations into the given Cartesian equations, we can express them in polar form.

For example, if we have the equation x - y = 2, we can substitute x and y with their respective polar forms:

r * cos(θ) - r * sin(θ) = 2

By rearranging this equation, we can obtain the equation in the form r = f(θ), where f(θ) represents the function of θ.