anubis01 said:Oh okay so I can say z=3cos[tex]\phi[/tex]
and from there plug in the values to find the [tex]\phi[/tex] bound to be cos(1/3)-1<[tex]\phi[/tex]<cos(2/3)-1 and the [tex]\theta[/tex] bound should just be 0< [tex]\theta[/tex]<2[tex]\pi[/tex]
anubis01 said:oh so then phi bound should be 0<[tex]\phi[/tex]<[tex]\pi[/tex] and since y=3cos[tex]\theta[/tex] the bounds for [tex]\theta[/tex] are
cos(1/3)-1<[tex]\theta[/tex]<cos(2/3)-1
anubis01 said:alright i think i got it now. So bound for theta 0<[tex]\theta[/tex]<2[tex]\pi[/tex]
y=3cos[tex]\phi[/tex] the bounds for phi are then
cos(1/3)-1<[tex]\phi[/tex]<cos(2/3)-1
and the parametric equation for x=3sin[tex]\phi[/tex]cos[tex]\theta[/tex]
and z=3sin[tex]\phi[/tex]sin[tex]\theta[/tex]
The parametric equation for a sphere is given by x = r sinθ cosφ, y = r sinθ sinφ, and z = r cosθ, where r is the radius of the sphere, θ is the polar angle, and φ is the azimuthal angle.
The parametric equation of a sphere is derived by using the spherical coordinate system, where the radius r, polar angle θ, and azimuthal angle φ are used to locate points on the surface of a sphere.
The parametric equation of a sphere allows for a more efficient way of representing points on the surface of a sphere, as it only requires two variables (θ and φ) instead of three (x, y, and z). It also allows for easier calculations and visualizations in three-dimensional space.
Yes, the parametric equation of a sphere can be used in various fields such as computer graphics, physics, and engineering, as it provides a convenient way to represent points on a spherical surface.
The standard equation of a sphere, x² + y² + z² = r², represents a sphere in Cartesian coordinates, while the parametric equation x = r sinθ cosφ, y = r sinθ sinφ, and z = r cosθ represents it in spherical coordinates. The parametric equation allows for a more flexible and versatile representation of a sphere, as it can easily be transformed and manipulated in 3D space.