Introduction to Polar Coordinates Calculator:
Polar Coordinates Calculator is a wonderful online source that helps you find polar coordinates from the given geometric coordinates. It is used to convert the rectangle or cartesian coordinates into polar coordinates in a simplified way.
The polar coordinate calculator is a beneficial tool for students, teachers, and professionals to make notes, assignments, projects, or research work in a few seconds without any man-made mistakes.
What is Polar Coordinates?
Polar coordinates are the geometry coordinate system that represents the point value in a plane using a distance and angle value. The distance value of polar coordinates is represented with r which is the value of origin and the angle is denoted with θ at the x-axis and y-axis.
It is useful in various fields like math for circular motion, engineering for AC circuits and signal processing, and graphic designing for imaging circular or spherical objects.
Polar Coordinates in Geometric Coordinates:
The polar coordinates value for geometric objects depends on the distance value which is the origin along the graph and the angle value along the positive axis at the origin. The formula used by the Polar Coordinates Calculator is given below,
$$ x \;=\; r . cos\;(\theta) $$
$$ y \;=\; r . sin\;(\theta) $$
How to Calculate the Polar Coordinates?
For the calculation of the polar coordinates, the polar coordinates graphing calculator converts the rectangle or carestain coordinates in geometry. For this, you need to know how to convert the coordinates of a cartesian or rectangle into polar coordinates.
Here is the guide on how the polar coordinate system calculator does the polar coordinates conversion and gives an accurate solution.
Step 1:
Identify the given problem whether it belongs to rectangle coordinates or cartesian coordinates.
Step 2:
Apply the rule of both rectangle or cartesian coordinates for the conversion of polar coordinates value.
$$ cos(\theta) \;=\; \frac{x}{r}\; x \;=\; r\; cos(\theta) $$
$$ sin(\theta) \;=\; \frac{y}{r}\; y \;=\; r\; sin(\theta) $$
$$ tan(\theta) \;=\; \frac{y}{x}\; x^2 + y^2 \;=\; r^2 $$
Step 3:
Add the given value as per the given problem for the polar coordinates value.
Step 4:
Lastly, simplify the above expression to find the distance value r and the angle value θ along both the x-axis or y-axis. The polar coordinates converter while the last steps make clear that each value is successfully calculated.
Practical Example of Polar Coordinates:
The polar coordinates calculator helps you to understand the calculation process so, let's understand how to convert cartesian coordinates to polar coordinates manually with the help of an example.
Example: Find polar coordinates using cartesian coordinates (-3,-4).
Solution:
The given cartesian coordinates are,
$$ x \;=\; -3,\; y \;=\; -4 $$
Use the Pythgeogan theorem to find the distance value of r,
$$ x^2 + y^2 \;=\; r^2 $$
Put the values in it,
$$ (-3)^2 + (-4)^2 \;=\; r^2 $$
$$ 9 + 16 \;=\; r^2 $$
$$ 25 \;=\; r^2 $$
$$ r \;=\; 5 $$
For angle θ, Put the cartesian value in the below equation,
$$ cos(\theta) \;=\; \frac{x}{r} $$
Put x = -3 ,r = 5,
$$ \theta \;=\; cos^{-1} \left( \frac{-3}{5} \right) \approx 2.214 $$
The polar coordinates of this point are,
$$ (r,θ) \;=\; (5,4.069) $$
How to Use Polar Coordinates Calculator?
The polar coordinate calculator has a simple interface so that you can use it to calculate the polar coordinates from the given cartesian or rectangle coordinates.
Before giving the input value, you must follow some instructions so that you do not face any inconvenience while using the polar coordinates graphing calculator. These steps are:
- Choose the type of coordinates from the given list.
- Enter the coordinates value that you want to find for polar coordinates in the input field.
- Review your input value because if it is not true that means it does not give you the solution of the polar coordinates value.
- Click the “Calculate” button to get the result of the given polar coordinates value in the polar coordinate system calculator.
- Click on the “Recalculate” button to get a new page for solving more problems of calculating the polar coordinates value.
Final Result of Polar Coordinate Calculator:
Polar Coordinates Calculator gives you the solution of the given coordinates value when you add the input into it. It gives you solutions with complete detail. It may contain as
- Result option of the polar equation calculator gives you a solution for the geometric coordinates value problems.
- Possible step provides you solution in polar coordinates in steps.
Advantages of Polar Coordinates Graphing Calculator:
The graphing calculator for polar coordinates will give you tons of advantages whenever you use it to calculate the polar coordinates value solution. These advantages are:
- The polar coordinates converter saves the time and effort that you consume in finding the geometric coordinates value solution manually.
- It is a free-of-cost tool so you can use it for free to do the polar coordinates conversion from the given coordinates value.
- Polar coordinate converter is a versatile tool that allows you to solve rectangle and carestain coordinates values.
- You can use this calculator for practice so that you may be familiar with the concept of the polar coordinates method.
- Polar equation calculator is a trustworthy tool that provides you with an accurate solution every time whenever you use it to find the polar coordinates of a given problem.
- Polar Coordinates Calculator allows you to find polar coordinates value as many times as you want.
