   Chapter 11, Problem 69RE

Chapter
Section
Textbook Problem

# Cylindrical-to-Rectangular Conversion In Exercises 69 and 70, find an equation in rectangular coordinates for the surface represented by the cylindrical equation, and sketch its graph. z = r 2 sin 2 θ + 3 r cos θ

To determine

To calculate: Thepoint (100,π6,50) inspherical coordinates from cylindrical coordinates.

Explanation

Given:

The point in cylindrical coordinates is (100,π6,50).

Formula used:

The conversion equations to convert a point (r,θ,z) from cylindricalcoordinates to spherical coordinates (ρ,θ,ϕ) are,

ρ=r2+z2,θ=θ,ϕ=arccos(zr2+z2)

Calculation:

Consider the given point,

(100,π6,50)

Compare it with (r,θ,z). Thus,

r=100,

θ=π6,

And,

z=50

Substitute the above values of r, θ and z in the cylindrical to spherical conversion equations and simplify them as,

ρ=r2+z2

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