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Chapter 9: Q. 5 (page 746)

This problem concerns the connections between the polar plane and the 胃r-plane.

(a) Which points in the 胃r-plane correspond to the pole in the polar plane, and why?

(b) Which points in the 胃r-plane correspond to the horizontal axis in the polar plane, and why?

(c) Which points in the 胃r-plane correspond to the vertical axis in the polar plane, and why?

Short Answer

Expert verified

a)胃,0corresponds to the pole.

b) 0,r,蟺,-rcorresponds to the points on the horizontal axis.

c)蟺2,r,3蟺2,-rcorresponds to points on the vertical axis.

Step by step solution

01

Step 1. Given information

Two different planes: polar plane and胃rplane.

02

Part (a) Step 1.  Find the points in the θr-plane correspond to the pole in the polar plane 

The pole in polar form is the point where r=0

So the point in胃rplane islocalid="1653109322792" 0,0

03

Part (b) Step 1. Find points in the θr-plane correspond to the horizontal axis in the polar plane:

In the polar plain the points on horizontal axis is r,0,-r,蟺

In 胃rplane these points correspond to point0,r,蟺,-r

04

Part (c) Step 1. Find points in the θr-plane correspond to the vertical axis in the polar plane.

In polar plane the points on vertical lines are r,蟺2,-r,3蟺2

In 胃rplane that points corresponds to the point蟺2,r,3蟺2,-r

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