   Chapter 10.4, Problem 112E

Chapter
Section
Textbook Problem

# True or False? In Exercises 113-116, determine whether the statement is true or false. If it is false, explain why or give an example that shows it Is false.If ( r , θ 1 ) and ( r , θ 2 ) represent the same point on the polar coordinate system, then θ 1 = θ 2 + 2 n π for some integer n.

To determine
Whether the given statement “If (r1,θ1) and (r2,θ2) represent the same point on the polar coordinate system, then θ1=θ2+2nπ for some integer n” is true or false.

Explanation

The point in the coordinates plane can be located in the form of polar coordinates (r,θ). In which r is directed distance from origin to point and θ is the directed angle that is taken counterclockwise from polar axes to the line segment and it is joining origin and the point.

As it is given that the same point is represented by two different polar coordinates (r1,θ1) and (r2,θ2).

It is known that if a revolution of 2π is taken then the same line or point is reached..

If n is some integer, then the revolution of 2nπ will create the same effect

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