Question

Convert the point (3,4,5) from Cartesian to spherical coordinates​

Answer 1

Answer:

spherical coordinates (5,tan^-1 (4/3),5)

Step-by-step explanation:

spherical coordinate (r,thita,z)

$r { }^{2} = x {}^{2} + y {}^{2}$

$\tan(thita ) = y \div x$

z=z

Answer 2

Answer:

Concept:

The placement of points in space can be easily described using the Cartesian co - ordinates. However, some surface can be challenging to represent using equations based on the Cartesian system. This is a well-known issue; keep in mind that, particularly in situations involving circles, polar coordinates can offer a helpful alternate system for defining the location of a point in the plane in 2 dimensions. In this part, we examine two distinct approaches of representing the positions of points in space, both of which are based on polar coordinate extensions. As the name implies, calculating the capacity of a cylinder-shaped water tank or the flow rate of oil through a pipe can be done with the use of spherical coordinates.

Given:

Transform the coordinates of the point (3,4,5) from Cartesian to spherical.

Find:

Discover the response to the problem.

Answer:

As stated in writing: r is the distance from the origin to the point, ϕ is the angle that must be rotated around the positive z-axis in order to reach the point, θ is the angle from the positive z-axis, and ρ is the distance between the point and the z-axis.

A sphere with the simple equation r = c in spherical dimensions has the Cartesian equation x2 + y2 + z2 = c2. Laplace's equation and the Helmholtz equation, two significant partial differential equations that appear in numerous physical issues, provide the separation of variables in spherical coordinates.

$r=\sqrt{(x^{2} +y^{2}+z^{2} )}$

  $=\sqrt{(3^{2}+4^{2}+5^{2} )}$

  $=\sqrt{50}$

  $=7.07$

Θ $=cos^{-1} (\frac{z}{r} )$

   $=cos^{-1} (\frac{5}{\sqrt[5]{2} } )$

   $=45$°

Φ $=tan^{-1} (\frac{y}{x} )$

   $=tan^{-1} (\frac{4}{3} )$

   $=53$°

∴ (7.07,45⁰,53⁰)

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