Chapter 10: Q 23. (page 777)

Give the cylindrical and spherical coordinates for the point with rectangular coordinates $(1, 0, 0)$

Short Answer

Expert verified

Cylindrical coordinates are $(1, 0, 0)$ and spherical coordinates are $(1, 0, \frac{π}{2})$

Step by step solution

Given Information

The given coordinates in rectangular coordinates are $(1, 0, 0)$

Finding the cylindrical coordinates

It is given that $x = 1, y = 0, z = 0$

We know that $r = \sqrt{x^{2} + y^{2}}, θ = \tan^{- 1} \frac{y}{x}, z = z$

Substituting the values, we get

$r = \sqrt{1^{2} + 0^{2}}, θ = \tan^{- 1} \frac{0}{1}, z = 0$

$\Rightarrow r = 1, θ = 0 °, z = 0$

localid="1651608209346" $\Rightarrow (r, θ, z) = (1, 0, 0)$

Finding the spherical coordinates

We know that $ρ = \sqrt{x^{2} + y^{2} + z^{2}}, θ = \tan^{- 1} \frac{y}{x}, ϕ = \cos^{- 1} \frac{z}{\sqrt{x^{2} + y^{2} + z^{2}}}$

$\Rightarrow ρ = \sqrt{1^{2} + 0^{2} + 0^{2}}, θ = \tan^{- 1} \frac{0}{1}, ϕ = \cos^{- 1} \frac{0}{\sqrt{1^{2} + 0^{2} + 0^{2}}}$

$\Rightarrow ρ = 1, θ = 0 °, ϕ = \cos^{- 1} 0 °$

$\Rightarrow ρ = 1, θ = 0 °, ϕ = \frac{π}{2}$

$\Rightarrow (ρ, θ, ϕ) = (1, 0, \frac{π}{2})$

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Give the cylindrical and spherical coordinates for the point with rectangular coordinates $(1, 0, 0)$

Short Answer

Step by step solution

Given Information

Finding the cylindrical coordinates

Finding the spherical coordinates

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Give the cylindrical and spherical coordinates for the point with rectangular coordinates(1,0,0)

Short Answer

Step by step solution

Given Information

Finding the cylindrical coordinates

Finding the spherical coordinates

One App. One Place for Learning.

Most popular questions from this chapter

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Give the cylindrical and spherical coordinates for the point with rectangular coordinates $(1, 0, 0)$