Make conversions between rectangular (cartesian) and polar plane coordinates.
This calculator is used to convert square to polar coordinates and vice versa for a 2nd device. It indicates the step-by-step calculation for each conversions.
Polar coordinates constitute a point that is placed with appreciate to the beginning (0,0) and an angle from the origin inside the reference course. they may be written as (r, θ), such that:
Cartesian coordinates imply a factor in an XY-plane via a couple of numerical values. those coordinates are signed distances from a factor to 2 perpendicular directed traces. they're generally written as (x, y), such that:
Solution:
Data Given:
Calculations:
Step 1: Determine ‘r’
\(r = \sqrt{x^{2} + y^{2}}\)
\(r = \sqrt{6^{2} + 2^{2}}\)
\(r = \sqrt{36 + 4}\)
\(r = \sqrt{40}\)
\(r = 6.324555320336759\)
Step 1: Determine ‘θ’
\(θ = arctan (\dfrac{y}{x}\)
\(θ = arctan (\dfrac{2}{6}\)
\(θ = arctan (\dfrac{1}{3}\)
No, the polar coordinates of a point aren't unique. The motive is that every factor may be represented through countless polar coordinates in limitless approaches.
In polar coordinates, z represents the complicated quantity in polar form, such that: z = x + iy (where i (iota) = \(\sqrt{-1}\)
Where
The polar coordinate representation of 1 is given as:
\(1 = 1e^{i} 0\)
The same equation holds genuine for (1 = 1e^{i} 2π) due to the fact that sine and cosine are both periodic with the angle 2π.
