Question

The cartesian coordinates of a point are (1,0,0).Find the spherical polar coordinate of the point.
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Answer 1

Answer:

Explanation:The spherical polar coordinates represent the coordinates of points on the surface of a sphere in a covariant form. The coordinates of the point P in this system is represented by the radial vector r which is the distance from the origin to the point, the polar or zenith angle θ which is the angle the radial vector makes with respect to the z-axis and the azimuth or longitudinal angle ϕ which is which is the normal polar coordinate in the x − y plane as shown below in the figure.These co-ordinates are related to the rectangular coordinates x, y, and z through

x =rsinθcosφ y =rsinθsinφ z =rcosθ  

Spherical polar coordinates in terms of Cartesian coordinates are

Answer 2

given are the cartesian coordinates it is then changed into spherical polar coordinate.

Explanation:

• cartesian coordinates = (x,y,z)=(1,0,0)
• spherical coordinates=(r,[tex]\theta\\ [/tex],$\alpha$)
• relation between cartesian and spherical coordinate coordinates is
• $r^{2} =x^{2} +y^{2}$
• [tex]r^{2} =1^{2}+ 0^{2} =1\\ r=1[/tex]
• $tan\theta=\frac{y}{x}$
• [tex]tan\theta=\frac{0}{1}=0\\ \theta=0[/tex]
• $\alpha =z$
• $\alpha =0$
• therefore the spherical polar coordinate is (1,0,0)