the7joker7 said:Because my answer is negative, don't I add 2pi to get the correct positive answer, as is the law of angles in this format?
FTR, here's the right answer.
`[(-4.24264068712,-4.24264068712,3.67381906147E-16)]`
Spherical coordinates are a three-dimensional coordinate system that is commonly used in mathematics and physics to describe the position of a point in space. They consist of a radial distance from the origin, an angle measured from the positive z-axis, and an angle measured from the positive x-axis.
To convert from spherical coordinates to Cartesian coordinates, you can use the following equations:
x = r sinθ cosφ
y = r sinθ sinφ
z = r cosθ
where r is the radial distance, θ is the angle measured from the positive z-axis, and φ is the angle measured from the positive x-axis.
Spherical coordinates have several benefits, including simplifying calculations for objects with spherical symmetry and making it easier to describe the position of an object in space relative to a fixed point. They are also commonly used in fields such as astronomy and physics.
Yes, you can convert from Cartesian coordinates to spherical coordinates using the following equations:
r = √(x² + y² + z²)
θ = tan⁻¹(y/x)
φ = cos⁻¹(z/√(x² + y² + z²))
where x, y, and z are the coordinates in the Cartesian system.
Yes, spherical coordinates are used in various real-world applications, such as navigation systems, satellite tracking, and geographic information systems. They are also commonly used in physics and engineering to describe the position of objects in space or to solve problems involving spherical symmetry.