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Free Cartesian to Polar calculator - convert cartesian coordinates to polar step by step
- Polar Coordinates Calculator
- What Are Cartesian and Polar coordinates?
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This calculator is used to convert rectangular to polar coordinates and vice versa for a 2D system. It shows the step-by-step calculation for both conversions.
1.1 Polar Coordinates:
Polar coordinates represent a point that is positioned with respect to the origin (0,0) and an angle from the origin in the reference direction. They are written as (r, θ), such that: 1. r is the radial distance from the origin to point 2. θ is the angle between the x-axis and the line joining point with the origin.
1.2 Cartesian (Rectangular) Coordinates:
Cartesian coordinates indicate a point in an XY-plane by a pair of numerical values. These coordinates are signed distances from a point to two perpendicular directed lines. They are usually written as (x, y), such that: 1. X represents the horizontal distance from the origin (positive to the right, negative to the left). 2. Y represents the vertical distance from the origin (positive upwards, negative downwards
Example 01:
Solution: Data Given: 1. Vertical coordinate = y = 2 2. Horizontal coordinate = x = 6 Calculations: Step 1: Determine ‘r’ r=x2+y2r = \sqrt{x^{2} + y^{2}}r=x2+y2 r=62+22r = \sqrt{6^{2} + 2^{2}}r=62+22 r=36+4r = \sqrt{36 + 4}r=36+4 r=40r = \sqrt{40}r=40 r=6.324555320336759r = 6.324555320336759r=6.324555320336759 Step 1: Determine ‘θ’ θ=arctan(yxθ = arctan (\dfrac{y}{x}θ=arctan(xy θ=arctan(26θ = arctan (\dfrac{2}{6}θ=arctan(62 θ=arctan(13θ = arctan (\dfrac{1}{3}θ=arctan(31
Example 2
Solution: Data Given: 1. r = 2 2. θ=45oθ = 45^\text{o}θ=45o Calculations: Step 1: Determine Horizontal Rectangular Component ‘x’ x=rcosθx = r cos θx=rcosθ x=2∗0.707x = 2 * 0.707x=2∗0.707 x=1.414x = 1.414x=1.414 Step 2: Determine Vertical Rectangular Component ‘y’ y=rsinθy = r sin θy=rsinθ y=2∗sin(45o)y = 2 * sin\left(45^\text{o}\right)y=2∗sin(45o)
Are polar coordinates unique?
No, the polar coordinates of a point are not unique. The reason is that each point can be represented by infinite polar coordinates in infinite ways.
What is z in polar coordinates?
In polar coordinates, z represents the complex number in polar form, such that: z = x + iy (where i (iota) = −1\sqrt{-1}−1 Where 1. x = Real part 2. y = Imaginary part
What is 1 in polar coordinates?
The polar coordinate representation of 1 is given as: 1=1ei01 = 1e^{i} 01=1ei0 The same equation holds true for 1=1ei2π1 = 1e^{i} 2π1=1ei2πdue to the fact that sine and cosine are both periodic with the angle 2π.
This polar coordinates calculator can handle all the conversions between coordinates including all ones listed in the above table, with the complete solution shown.
From the source of Wikipedia: Polar coordinate system, Conventions, Uniqueness of polar coordinates, Converting between polar and Cartesian coordinates. From the source of Math Insight: Conversion formulas, the plane of Cartesian coordinates, coordinates r and θ.
Jul 29, 2024 · The rectangular to polar coordinates calculator couldn't make converting from rectangular to polar coordinates easier. By just entering the x and y values of your problem, the calculator will instantly display the r and θ components of the polar coordinate representation of your point.
- Gabriela Diaz
Dec 22, 2023 · The Cartesian to Polar Coordinate Calculator effortlessly convert Cartesian coordinates (x, y) into polar coordinates (r, θ).
How do you convert polar coordinates to rectangular coordinates? The formula for conversion is x = r*cos(θ) and y = r*sin(θ) . Are there any advantages to using polar coordinates over rectangular coordinates?
This program converts rectangular coordinates into polar ones. Send feedback | Visit Wolfram|Alpha. Get the free "Coordinates: Rectangular to Polar" widget for your website, blog, Wordpress, Blogger, or iGoogle. Find more Mathematics widgets in Wolfram|Alpha.
This graph converts cartesian coordinates to polar coordinates for the interval [0,2π). Because there are multiple solutions to arctan for this interval, both values are shown.
