Question

The rectangular coordinates of a point are given. find polar coordinates of the point such that r > 0 and 0 ≤ θ < 2π.

(-1, 0)

Answer 1

The polar coordinates for the point (-1, 0) are (1, π), with r being the distance from the origin and θ the angle from the positive x-axis.

Step-by-step explanation:

To convert the Cartesian coordinates (-1, 0) into polar coordinates, we use the relationship between Cartesian and polar systems. The polar coordinates consist of a radial coordinate r which is the distance of the point from the origin, and an angle θ which is the angle the radial vector makes with the positive x-axis. To calculate r, we use the Pythagorean theorem:

r = √((-1)^2 + 0^2) = √(1) = 1

Since the point lies on the negative x-axis, the angle θ is π radians (180 degrees). Therefore, the polar coordinates are (r, θ) = (1, π) which satisfy the condition r > 0 and 0 ≤ θ < 2π.

To summarize, we have converted the ordered pair (-1, 0) to polar coordinates using the conversion formulas:

• x = r × cos(θ)
• y = r × sin(θ)

And we found that for the point (-1, 0), the polar coordinates are (1, π).