Question

1) Convert the point (x,y,z)=(−2,−3,−1) to cylindrical coordinates. Give answers as positive values, either as expressions, or decimals to one decimal place.
(r,θ,z) =

2) Convert the point (x,y,z)= (3,−2,−3) to spherical coordinates. Give answers as positive values, either as expressions, or decimals to one decimal place.
(ρ,θ,ϕ)=

3) Convert the equation ρ = 3 to rectangular coordinates and write in standard form.

Answer 1

1)

The rectangular coordinates are converted to rectangular coordinates by using the equatiions

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• 
• 

The cylindrical coordinates are :

2)

The rectangular coordinates are converted to spherical coordinates by using the equations:

• 
• 
• 

• 
• 
• 

The spherical coordinates are

3)

We have seen in the above equation that

is a sphere of radius 3 centered at the origin.