Coordinate Conversion Script (Rectangular <-> Polar)

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This JavaScript code provides functionality for converting coordinates between rectangular (Cartesian) and polar coordinate systems. It includes the following features: (No code changes need to be made in the script it's self)

• Input Validation: Checks for valid numerical inputs and the correct number of comma-separated values.
• Error Handling: Displays user-friendly error messages for invalid inputs.
• Conversion Formulas: Implements the standard formulas for both rectangular-to-polar and polar-to-rectangular conversions.
• Decimal Output: Displays the converted coordinates with a precision of four decimal places.
• Fractional Output: Displays the converted coordinates as fractions using the `math.js` library.
• Dynamic Display: Updates the 'results' HTML element with the converted coordinates.

Input forms at bottom

Functions

`toFraction(number)`

This function takes a number as input and converts it into a fractional representation using the `math.js` library. It returns a string in the format "numerator/denominator".

`convertPolarToRect()`

This function converts polar coordinates (radius, angle in degrees) to rectangular coordinates (x, y).

1. Retrieves Input: Reads the radius and angle values from the 'polarInputVal' input field. The input should be in the format "radius, angle".
2. Input Parsing: Splits the input string into two parts based on the comma delimiter.
3. Input Validation:
   • Checks if exactly two values are provided.
   • Verifies that the radius and angle are valid numbers.
4. Conversion:
   • Converts the angle from degrees to radians.
   • Calculates the x and y coordinates using the following formulas:
     • `x = cos(angleRad) * radius`
     • `y = sin(angleRad) * radius`
5. Output Formatting:
   • Formats the x and y coordinates to four decimal places using `toFixed(4)`.
   • Converts the x and y coordinates to fractions using the `toFraction()` function.
6. Result Display: Updates the 'results' HTML element with the calculated x and y coordinates, displaying both the decimal and fractional representations.

`convertRectToPolar()`

This function converts rectangular coordinates (x, y) to polar coordinates (radius, angle in degrees).

1. Retrieves Input: Reads the x and y values from the 'rectInputVal' input field. The input should be in the format "x, y".
2. Input Parsing: Splits the input string into two parts based on the comma delimiter.
3. Input Validation:
   • Checks if exactly two values are provided.
   • Verifies that the x and y values are valid numbers.
4. Conversion:
   • Calculates the radius using the formula: `r = sqrt(x^2 + y^2)`
   • Calculates the angle (theta) in radians using `atan2(y, x)`. The result is then converted to degrees.
   • Normalizes the angle to be within the range of 0 to 360 degrees.
5. Output Formatting:
   • Formats the radius and angle to four decimal places using `toFixed(4)`.
   • Converts the radius and angle to fractions using the `toFraction()` function.
6. Result Display: Updates the 'results' HTML element with the calculated radius and angle, displaying both the decimal and fractional representations.

Dependencies

• math.js: This library is used for converting numbers to fractions. It is in assets/links file path and is accessed via relative path.

Usage

1. Include this JavaScript code and the `math.js` library in your HTML file.
2. Create input fields with the IDs 'polarInputVal' and 'rectInputVal' for polar and rectangular coordinates, respectively.
3. Create a 'div' element with the ID 'results' to display the conversion results.
4. Call the `convertPolarToRect()` or `convertRectToPolar()` functions when the user submits the input.

Input correction

If you are confused on input forms read below. The following is true for the everything related to the converter.

• When using sqrt (square root) you need parenthisis around the number being sqrt -> sqrt(3)
• When using π you need to replace it with 'pi' -> pi
• If you use a mixed fraction, ensure you use the multiply symbole (**) rather than leaveing a sapce -> 3*pi/2
• Here is a example of a input that uses all three -> 7, sqrt(3)*pi/6