Polar Graphing Calculator

Step-by-Step Guide to Using the Polar Graphing Calculator

Step 1: Select the Polar Function Type

Begin by selecting the type of polar function you want to graph. In the calculator, locate the dropdown labeled Polar Function Type. You will see options such as:

• Circle (r = a)
• Cardioid (r = a(1 + cos(θ)))
• Rose (r = a*cos(nθ))
• Spiral (r = aθ)
• Lemniscate (r² = a²cos(2θ))

Select the function that best fits your requirements.

Step 2: Enter the Parameter (a)

Next, input the value for the parameter a in the field labeled Parameter (a). Ensure your value is within the allowed range of 0.1 to 100. This parameter will define the size and shape of your polar graph.

Step 3 (Optional): Specify the Number of Petals (n) for Rose Curve

If you selected the Rose function type in Step 1, you will need to specify the number of petals, n, by entering a number between 1 and 20 in the field labeled Number of Petals (n) – For Rose Curve. If you chose a different function type, you can skip this step.

Step 4: Define the Angle Range in Radians

Input the start and end angles for your graph in radians. For the Start Angle (θ), enter a value between 0 and 6.28318. For the End Angle (θ), provide a value anywhere from 0 to 12.56636. These settings will determine the portion of the graph displayed and calculated.

Step 5: Calculate Results

Once all required inputs are filled, the calculator will compute several important attributes of the polar graph, including:

• Radius (r): Based on the selected function and parameters.
• X Coordinate: Calculated using the formula r * cos(θ).
• Y Coordinate: Calculated using the formula r * sin(θ).
• Area Under Curve: The calculator integrates to find the area enclosed by the curve over the specified angle range.
• Arc Length: The length of the curve as it spans from the start to end angle.

These results will be displayed using the specified format, which may include decimals and units for clarity.