What is the range of theta in Spherical Coordinate System? - The Right Gate

What is the range of theta in Spherical Coordinate System?

What is the range of theta in Spherical Coordinate System?

What is the range of theta in Spherical Coordinate System?

Though theta is an angle, it can take value only up to 180o and not 360o. The reason is quite obvious. It is the minimum angle between the position vector of the point (r) and +Z axis.

Consider any point P present in the space. The position vector of this point i.e. r forms two angles with +Z axis, based on the nature of tracing, as shown in following figures. But, according to the definition, you should go with the minimum one as shown in figure.

 

What is the range of theta in Spherical Coordinate System?
Correct Theta
What is the range of theta in Spherical Coordinate System?
Wrong Theta

So, for any point around the Z axis, the angle made by the r with +Z axis is always less or equal to 180o .

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