   Chapter 11.7, Problem 6E

Chapter
Section
Textbook Problem

# Cylindrical-to-Rectangular Conversion In Exercises 3–8, convert the point from cylindrical coordinates to rectangular coordinates. ( 6 , − 3 π 2 , 2 )

To determine

To calculate: The rectangular coordinate of the point where the cylindrical coordinate of the point is (0.5,4π3,8).

Explanation

Given:

The cylindrical coordinate of the point is (0.5,4π3,8).

Formula used:

Conversion formula from cylindrical to rectangular coordinate,

x=rcosθy=rsinθz=z

Calculation:

The cylindrical coordinate is (r,θ,z)=(0.5,4π3,8).

Here, r=0.5,θ=4π3 and z=8.

Use conversion formula to convert the point in rectangular coordinate as below:

x=0.5cos(4π3)=0

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