   Chapter 10, Problem 59RE

Chapter
Section
Textbook Problem

Polar-to-Rectangular Conversion In Exercises 59-62, the polar coordinates of a point are given. Plot the point and find the corresponding rectangular coordinates for the point. ( 5 , 3 π 2 )

To determine

To graph: The point (5,3π2) and calculate the corresponding rectangular coordinates for the point.

Explanation

Given:

The given point is (5,3π2).

Graph:

Consider the ordered polar pair (5,3π2), now here r=5 and θ=3π2.

Now mark 5 units from origin on the r axis and in the same way mark 3π2 angle on θ axis.

Construct a perpendicular line from these points, so the point of intersection will be the ordered pair (5,3π2).

So, the graph is shown below:

Formula Used:

The formula to convert polar co-ordinates into rectangular co-ordinates are x=rocsθ,y=rsinθ.

Calculation:

Consider the provided coordinates: (5,3π2).

So, r=5, θ=3π2.

To convert this point into rectangular coordinates, use the relation:

x=rcosθ

y=rsinθ

Put the values of r and θ

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