Question

find a spherical coordinate EQUATIONS for the sphere x^2+y^2+(z-1)^2= 1 ​

Answer 1

Step-by-step explanation:

In summary, the formulas for Cartesian coordinates in terms of spherical coordinates are x=ρsinϕcosθy=ρsinϕsinθz=ρcosϕ

Answer 2

Answer:

r=2cosФ

Given :

sphere x^2+y^2+(z-1)^2= 1 ​

To find :

find a spherical coordinate EQUATIONS for the sphere x^2+y^2+(z-1)^2= 1 ​

Explanation :

We have

x^2+y^2+(z-1)^2= 1 ​

In spherical coordinates

x=r sinФcos∅

y=r sonФ sin∅

and z = r cosФ

Putting these values in equation we get

r² (sin²Фcos²∅+sin²Фsin²∅)+(r cosФ-1)²

r²sin²Ф+(r cosФ-1)²=1

r²sin²Ф+r²cos²Ф+1-2rcosФ=1

r²-2rcosФ=0

r(r-2cosФ)=0

But since

r$\neq$0

r-2cosФ=0

r=2cosФ

To know more about  spherical coordinates refer:

https://brainly.com/question/4465072

https://brainly.com/question/29644950

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