Coordinate Systems Calculator

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Example

Created on 2024-06-20Asked by William Hernandez (Solvelet student)

Convert the Cartesian coordinates

(3, 4)

to polar coordinates.

Solution

Step 1: Identify the Cartesian coordinates

(3, 4)

. Step 2: Use the formulas for converting Cartesian to polar coordinates:

r = \sqrt{x^2 + y^2}, \quad \theta = \arctan\left(\frac{y}{x}\right).

Step 3: Substitute the coordinates:

r = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5,

\theta = \arctan\left(\frac{4}{3}\right).

Step 4: Compute the angle:

\theta \approx \arctan\left(\frac{4}{3}\right) \approx 0.93 \text{ radians}.

Step 5: Conclusion. The polar coordinates corresponding to

(3, 4)

are

(5, 0.93)

. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Jackson Williams on Solvelet

1. Convert the Cartesian coordinates

(3, 4)

to polar coordinates 2. Convert the spherical coordinates

(r = 2, \theta = \frac{\pi}{3}, \varphi = \frac{\pi}{4})

to Cartesian coordinates.,

DefinitionCoordinate systems are a kind of mathematical model that establishes the position and orientation of points and objects within a space. Some coordinate systems are: Cartesian coordinates, polar coordinates, cylindrical coordinates, spherical coordinates. Each system has its axes and measures the distances and angles. In mathematics, physics, engineering, geography, and other disciplines, a coordinate system is a spec... Most of the time these are the standard form of representing spatial information in various contexts. Example: Latitude and longitude are angular measurements that specify a location on the Earth's surface in degrees of angle from the equator and the Prime Meridian in such coordinate system.

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