How do you determine angle phi in spherical coordinates?

Thread starter Chandasouk
Start date Dec 14, 2010
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Angle Coordinates Phi Spherical Spherical coordinates

In summary, the angle phi in spherical coordinates is used to specify the position of a point in three-dimensional space in relation to a reference point or axis. It is measured in radians with a range of 0 to 2π or 0 to 360 degrees and represents the angle formed between the reference axis and the projection of the point onto the xy-plane. The x and y coordinates of a point in spherical coordinates are related to angle phi with specific formulas, and it can be calculated using the inverse tangent function. Angle phi can also be negative, representing the rotation of a point around the z-axis.

Dec 14, 2010

Chandasouk

In general, how do I determine the angle phi when you have to use spherical coordinates for integration?

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Dec 14, 2010

fss

Erm... you have to decide on a range that makes sense for the problem.

Related to How do you determine angle phi in spherical coordinates?

1. What is the purpose of determining angle phi in spherical coordinates?

The angle phi, also known as the azimuthal angle, is used to specify the position of a point in three-dimensional space in relation to a reference point or axis. In spherical coordinates, it is used to locate a point in terms of its distance from the origin, its polar angle, and its azimuthal angle.

2. How is angle phi measured in spherical coordinates?

Angle phi is measured in radians, with a range of 0 to 2π, or 0 to 360 degrees. It represents the angle formed between the reference axis and the projection of the point onto the xy-plane.

3. What is the relationship between angle phi and the x and y coordinates in spherical coordinates?

In spherical coordinates, the x and y coordinates of a point are related to the angle phi as follows: x = r*sin(theta)*cos(phi) and y = r*sin(theta)*sin(phi), where r is the distance from the origin and theta is the polar angle.

4. How do you calculate angle phi in spherical coordinates?

To calculate angle phi, you can use the inverse tangent function, also known as arctan, with the x and y coordinates of the point. The formula is phi = arctan(y/x), where x and y are the coordinates of the point in the xy-plane.

5. Can angle phi be negative in spherical coordinates?

Yes, angle phi can be negative in spherical coordinates, as it represents the rotation of a point around the z-axis. A positive value indicates a rotation in the counterclockwise direction, while a negative value represents a rotation in the clockwise direction.