Question

B) find the cylindrical coordinates of the points where the cartesian coordinates are i) (6,6,8) ii) (✓2,1,1 )

Answer 1

Given: Cartesian coordinates i) (6,6,8) and ii) (√2,1,1 ).

To find: The cylindrical coordinates of the points.

Solution:

• Now we know that the relation between cartesian coordinate and cylindrical coordinate is:

         r² = x² + y²

         tanФ = y / x

        z = z

        (i) x = 6, y = 6, z = 8

           r² = (x² + y²)

           r = 6√2

          Ф = π/4

          z = 8

• So the cylindrical coordinates are (6√2, π/4, 8)

         (ii) x = √2, y = 1, z = 1

         r² = (x² + y²)

         r = √3

        Ф = 0.615 rad

         z = 1

• So the cylindrical coordinates are (√3, 0.615, 1)

Answer:

               The cylindrical coordinates of the points where the cartesian coordinates are (6,6,8) is (6√2, π/4, 8) and (✓2,1,1 ) is (√3, 0.615, 1).