Question

Write the rectangular equation in polar form... x=3

Answer 1

r = 3, theta = 0

Answer 2

rcosθ = 3

r = 3secθ

Answer 3

[AI-generated answer — Explain Bot]

To write the rectangular equation x = 3 in polar form, we need to express x in terms of radius (r) and angle (θ).

In rectangular coordinates, x represents the horizontal position on the x-axis. So, x = 3 simply means that the point lies at a constant horizontal position of 3 on the x-axis, regardless of the vertical position.

In polar coordinates, a point is represented by its distance from the origin (r) and the angle it forms with the positive x-axis (θ). To convert x = 3 into polar form, we can consider that the point lies on a vertical line passing through x = 3.

Since x = 3 is a horizontal line, the vertical position of the point can vary. This corresponds to different values of the radius (r) in polar coordinates. Therefore, in polar form, we can write the equation as rθ, where r represents the radius and θ represents the angle.

Since the point lies at a constant horizontal position of 3, the angle θ can take any value. Thus, the equation in polar form is rθ, where r is any non-negative value and θ is any real number.