Parametric Equation Calculator

Using the Parametric Equation Calculator

The Parametric Equation Calculator is designed to help you compute the X and Y positions of a point using parametric equations, and to calculate its distance from the origin and the angle it makes with the X-axis. Follow the steps below to use the calculator effectively:

Step 1: Enter the Coefficients

• X-coefficient (a): Enter the coefficient for x(t) in the input field labeled “X-coefficient (a).” This field is required and must be a number between -100 and 100, with increments of 0.1.
• Y-coefficient (b): Similarly, enter the coefficient for y(t) in the input field labeled “Y-coefficient (b).” This value is also required, and must fall within the same range and step as the X-coefficient.

Step 2: Enter the Frequencies

• X-frequency (ω₁): In the input field labeled “X-frequency (ω₁),” enter the frequency value for x(t). It is required and must be a number between -100 and 100, with a step of 0.1.
• Y-frequency (ω₂): Input the frequency value for y(t) in the field labeled “Y-frequency (ω₂).” It should adhere to the same validation rules as the X-frequency.

Step 3: Enter the Phases

• X-phase (φ₁): Enter the phase value for x(t) in degrees in the field labeled “X-phase (φ₁).” Make sure this required value is between -360 and 360, and respects a step of 0.1.
• Y-phase (φ₂): Similarly, enter the phase value for y(t) in degrees in the field labeled “Y-phase (φ₂).” Follow the same validation criteria as for X-phase.

Step 4: Enter the Time Value

Time (t): Enter the time value in the field labeled “Time (t).” This value is required and must be between 0 and 100, with a step of 0.1.

Step 5: Understand the Output

• X Position: The calculator computes the X position using the formula: xCoeffT * cos(xFreqT * tValue + (xPhaseT * pi/180)). It is presented as a number rounded to four decimal places.
• Y Position: Similarly, the Y position is computed using: yCoeffT * cos(yFreqT * tValue + (yPhaseT * pi/180)), rounded to four decimal places.
• Distance from Origin: The calculator determines the distance from the origin using the formula: sqrt(pow(xPosition, 2) + pow(yPosition, 2)). This is also rounded to four decimal places.
• Angle (degrees): Finally, the angle which the line from the origin to the point makes with the X-axis is calculated using: atan2(yPosition, xPosition) * 180/pi. The result is rounded to two decimal places and expressed in degrees.

By following the steps above, you can effectively use the Parametric Equation Calculator to analyze parametric equations with ease.