Generate parametric equations graphically with this calculator. Customize variables, constants, and labels easily.

Parametric Equation

Purpose

The Parametric Equation function in this web app allows you to input mathematical expressions for x and y coordinates in terms of a variable (usually denoted as theta) to create a parametric plot. This function helps visualize curves and shapes based on mathematical equations.

Use Cases

• Visualizing curves and shapes based on mathematical equations
• Creating custom plots with specific x and y coordinates

How to Use

1. Enter the mathematical expression for the x-coordinate in the X Equation field.
2. Enter the mathematical expression for the y-coordinate in the Y Equation field.
3. Adjust the range of the variable using the Start Value and Stop Value fields.
4. Optionally, you can add constants to the equations by filling in the Constant 1, Constant 2, etc. fields.
5. Click on the Plot button to generate the parametric plot.

Input Values

1. X Equation: Mathematical expression for the x-coordinate
2. Description: Enter the equation for the x-coordinate in terms of the variable.
3. Y Equation: Mathematical expression for the y-coordinate
4. Description: Enter the equation for the y-coordinate in terms of the variable.
5. Start Value: Start value for the variable
6. Description: Initial value for the variable in the equations.
7. Stop Value: Stop value for the variable
8. Description: Final value for the variable in the equations.
9. Constant 1, Constant 2, etc.: Constants for the equations
10. Description: Optional constants that can be added to the equations.

Output Values

1. Plot: Parametric plot of the x and y coordinates
2. Description: Visual representation of the mathematical equations in a plot.

Any other Instruction

• Adjusting the range of the variable can change the shape of the plot.
• Experiment with different equations and constants to create unique plots.

Steps of Calculation

1. Precheck the input equations.
2. Generate a range of values for the variable.
3. Replace any constants in the equations.
4. Evaluate the x and y coordinates for each value of the variable.
5. Plot the parametric curve based on the calculated coordinates.

Technical Parameter names

x, y, variable, variable_start, variable_stop, variations, x_label, y_label, title, const_1, const_1_part, const_2, const_2_part, const_3, const_3_part, const_4, const_4_part, const_5, const_5_part, aspect

Return Values

Plot

Example Expressions

You can use the following expressions to directly evaluate in a non interactive manner using eva():

1. X Equation: '2cos(theta)', Y Equation: '3sin(theta)', Start Value: 0, Stop Value: 6.28
2. X Equation: 'cos(theta)', Y Equation: 'sin(2*theta)', Start Value: 0, Stop Value: 6.28

Click on Help icon to open the help page on a separate window.