Convert to Rectangular Coordinates Calculator Online

The Convert to Rectangular Coordinates Calculator is a powerful tool designed to convert polar coordinates to rectangular coordinates. This conversion is essential in various fields, including mathematics, physics, and engineering. The calculator utilizes a straightforward formula:

x = r * cos(θ) y = r * sin(θ)

Here:

• r is the magnitude or distance from the origin to the point,
• θ (theta) is the angle measured counterclockwise from the positive x-axis to the line segment connecting the origin to the point, and
• x and y are the rectangular coordinates of the point.

Formula of Convert to Rectangular Coordinates Calculator in Detail

The formula breaks down the conversion process, providing a clear understanding of how the calculator derives rectangular coordinates from polar coordinates. This mathematical transformation is fundamental in visualizing and analyzing spatial relationships.

To further assist users, here’s a table of general terms related to polar and rectangular coordinates commonly searched:

Term	Definition
Polar Coordinates	Coordinates represented by (r, θ), where r is magnitude and θ is angle.
Rectangular Coordinates	Coordinates represented by (x, y) on a Cartesian plane.
Magnitude (r)	Distance from the origin to the point in polar coordinates.
Angle (θ)	Counterclockwise rotation from the positive x-axis to the line segment connecting the origin to the point.

Example of Convert to Rectangular Coordinates Calculator

Let’s consider an example to illustrate the practical application of the Convert to Rectangular Coordinates Calculator.

Suppose we have polar coordinates (r = 5, θ = 45 degrees). Using the formula, we can calculate the rectangular coordinates:

x = 5 * cos(45) ≈ 3.54 y = 5 * sin(45) ≈ 3.54

Therefore, the rectangular coordinates are approximately (3.54, 3.54).

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