Polar Coordinates Calculator

A Polar Coordinates Calculator is a tool used to calculate the polar coordinates of a point in a two-dimensional plane, given its rectangular (Cartesian) coordinates. Polar coordinates are a way of describing the position of a point in terms of its distance from the origin (radius) and the angle it forms with the positive x-axis (angle or azimuth).

The Polar Coordinates Calculator typically requires the user to input the x and y coordinates of the point, and then calculates the corresponding radius and angle. The calculator can display the results in either degrees or radians, depending on the user’s preference.

Formula for Polar Coordinates

The formula for converting rectangular (Cartesian) coordinates (x, y) to polar coordinates (r, θ) is:

r = √(x² + y²)

θ = arctan (y/x)

where:

• r is the distance from the origin to the point (also known as the radius)
• θ is the angle formed between the positive x-axis and the line connecting the origin and the point (also known as the angle or azimuth)
• x is the x-coordinate of the point
• y is the y-coordinate of the point
• arctan is the inverse tangent function

Example Calculation

Suppose we have a point P with coordinates (2, 3) in a Cartesian plane. We want to find its polar coordinates (r, θ).

First, we can calculate the radius r as: r = √(2² + 3²) = √13 ≈ 3.605

Then, we can calculate the angle θ as: θ = arctan (3/2) ≈ 56.31°

Therefore, the polar coordinates of the point P are approximately (3.605, 56.31°).

How to use the Polar Coordinates Calculator

To use the Polar Coordinates Calculator, follow these steps:

1. Input the x and y coordinates of the point you want to convert to polar coordinates.
2. Click the “Calculate” button to execute the calculation.
3. The calculator will display the resulting radius and angle (in either degrees or radians).

FAQs

What is the difference between Cartesian and polar coordinates?

Cartesian coordinates describe the position of a point in terms of its x and y coordinates, whereas polar coordinates describe the position in terms of its radius and angle.

How do you convert polar coordinates to Cartesian coordinates?

To convert polar coordinates (r, θ) to Cartesian coordinates (x, y), use the following formulas: x = r * cos(θ) y = r * sin(θ)

What is the range of values for polar coordinates?

The radius (r) is always a positive value, and the angle (θ) can range from 0 to 360 degrees (or 0 to 2π radians), depending on the convention used.