Question

Different Coordinate Systems As was noted in the overview of the chapter, certain curves are more naturally described in one coordinate system than in another. In each of the following situations, which coordinate system would be appropriate: rectangular or polar? Give reasons to support your answer.

(a) You need to give directions to your house to a taxi driver.
(b) You need to give directions to your house to a homing pigeon.

Short answer

(a).A rectangular coordinate system would be appropriate to give directions to a taxi driver.

(b).A polar coordinate system would be appropriate to give directions to a homing pigeon.

Step-by-step solution

Step 1.Given onformation.

A picture of a residential area with grids and marked directions.

Step 2.  The coordinate system to be used by a taxi driver.

We will check if a taxi driver can travel at an angle and thus recommend a rectangular or a polar coordinate accordingly.

A taxi cannot drive at angles.

Thus, it can cover the distance only by covering the distance in straight lines without any angles.

Since it cannot drive at an angle to cover the distance, it is appropriate to give directions using a rectangular coordinate system.

Step 1.Given information.

A picture of a residential area with grids and marked directions.

Step 2. The coordinate system to be used by a homing pigeon.

We will check if a pigeon can travel at an angle and thus recommend a rectangular or a polar coordinate accordingly.

A pigeon can fly at any angle.
Thus, it can cover the distance easily and in a short time by flying at an angle.
Since it requires an angle to cover the distance, it is appropriate to give directions using a polar coordinate system.