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Give the rectangular and spherical coordinates for the point with cylindrical coordinates:

48,π3,4

Short Answer

Expert verified

Rectangular coordinates are23,6,4and spherical coordinates are8,π3,π3

Step by step solution

01

Given Information

The given expression isr,θ,ϕ=48,π3,4

02

Finding the rectangular coordinates

As r=48,θ=π3,ϕ=4

To find out rectangular coordinates, we will use

x=rcosθ,y=rsinθ,z=z

Using the values

x=48cosπ3,y=48sinπ3,z=4

x=23,y=6,z=4

x,y,z=23,6,4

03

Finding the spherical coordinates

To convert rectangular to spherical coordinates

ρ=r2+z2,θ=θ,ϕ=tan-1rz

Putting the values

ρ=482+42,θ=π3,ϕ=tan-1484

ρ=48+16,θ=π3,ϕ=tan-13

ρ=64,θ=π3,ϕ=π3

ρ=8,θ=π3,ϕ=π3

ρ,θ,ϕ=8,π3,π3

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