Point (2, π/3) in polar coordinates translates to point (1, sqrt(3)) in rectangular coordinates.
Plotting and Converting Polar Coordinates to Rectangular Coordinates
Converting polar coordinates to rectangular coordinates involves understanding the relationship between the two systems. In polar coordinates, a point is described by its distance from the origin (r) and the angle it forms with the positive x-axis (θ). In rectangular coordinates, a point is described by its horizontal (x) and vertical (y) distances from the origin.
Plotting the Point (2, π/3):
1. Identify the radius (r): In this case, r = 2.
2. Identify the angle (θ): θ = π/3.
3. Convert angle to degrees (optional): If needed, convert the angle to degrees: 180° * (π/3) / π = 60°.
4. Calculate x and y coordinates:
* x = r * cos(θ) = 2 * cos(π/3) = 1
* y = r * sin(θ) = 2 * sin(π/3) = √3
5. Plot the point: Mark the point (1, √3) on the coordinate plane.
Here's the graph:
[Image of the point (1, √3) plotted on a coordinate plane]
Therefore, the rectangular coordinates of the point (2, π/3) are (1, √3).
Addtional Notes:
* The positive x-axis corresponds to a polar angle of 0°, and the positive y-axis corresponds to a polar angle of 90°.
* As the angle increases counter-clockwise, we move around the origin in a circular path.
* The distance from the origin (r) remains constant for a specific point, regardless of the angle.