Find the rectangular coordinates of the point whose spherical coordinates are given. (a) (3, 0, π/2) (x, y, z) = ( (x, y, z) = ( I ) (b) (4, π/3, π/4)
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- Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?Which lines or line segments or rays must be drawn or constructed in a triangle to locate its a orthocenter? b centroid?Find the position of a point given as (5, 2π/3, 2) in cylindrical coordinates, in cartesian and spherical coordinates.
- Find an equation in spherical coordinates for the surface represented by the rectangular equation x2 + y2 − 3z2 = 0Find the rectangular coordinates of the point P with cylindrical coordinates (r, θ, z) = (5, 5π/4, 6).Find an equation in spherical coordinates for the surface represented by the rectangular equation x2 + y2 = 2z2
- Provide the equation of a sphere of radius 5, centered at the origin, in: 1. rectangular coordinates 2. cylindrical coordinates 3. spherical coordinatesConvert (r, θ , z) =(3, π/6 , 4)from cylindrical to spherical coordinates.Find the spherical coordinates of the point that has rectangular coordinates (x, y, z) = (4,−4, 4 √ 6)
- What are the cylindrical coordinates of the point whose rectangular coordinates are (x = -1, y = 4, z = -3)?Find an equation in spherical coordinates whose graph is the parapoloid Z=(X^2)+(Y^2)Plot the point whose spherical coordinates are (ρ, φ, θ) = (2, π/3, π/4) and give its rectangularcoordinates.