Polar Graph Calculator

The Polar Graph Calculator allows users to compute the X and Y coordinates, polar area, and arc length for various polar graph types by entering the radius and angle values.

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How to Use the Polar Graph Calculator

This Polar Graph Calculator is designed to help you plot and analyze polar graphs with ease. Please follow the steps below to effectively use the calculator:

Step 1: Enter the Radius

To begin, locate the Radius (r) input field. Enter a positive numerical value that represents the radius of your polar plot. Note that this field is required, and the minimum value you can enter is 0. You have the option to enter values in increments of 0.1 for more precise measurements.

Step 2: Enter the Angle

Next, find the Angle θ (in degrees) input field. Here, you will input the angle in degrees. Ensure the value is within the range of 0 to 360, as these are the valid input limits. Remember to enter angle values in whole numbers since the step interval is 1 degree.

Step 3: Select the Polar Graph Type

Proceed to the Polar Graph Type dropdown menu. This field is also mandatory. Select the type of polar graph you wish to plot from the available options:

  • Circle (r = a)
  • Rose Curve (r = a·cos(nθ))
  • Spiral (r = a·θ)
  • Cardioid (r = a(1 + cos(θ)))

Selecting the appropriate graph type will influence how your inputs are calculated and visualized.

Step 4: Review Calculated Results

Once you have inputted the necessary values, the calculator will compute the results automatically. Here are the output fields you will see:

  • X Coordinate: Calculated using the formula radius * cos(theta * π / 180). The result is rounded to three decimal places.
  • Y Coordinate: Calculated using the formula radius * sin(theta * π / 180). The result is displayed with three decimal points of precision.
  • Area (sector): Given by the formula 0.5 * radius² * (θ * π / 180). The area is displayed in square units with two decimal places.
  • Arc Length: Determined by the formula radius * (θ * π / 180). The arc length is shown in units with two decimal places.

Conclusion

By following these steps, you can efficiently utilize the Polar Graph Calculator to explore various polar graph types, calculate coordinates, sector areas, and arc lengths. Ensure all required fields have valid inputs to obtain accurate results.