   Chapter 10.4, Problem 115E

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 x > 0 , then the point (x, y) on the rectangular coordinate system can be represented by ( r , θ ) on the polar coordinate system, where r = x 2 + y 2 and θ = arctan ( y / x ) .

To determine
Whether the given statement “If x>0, then the point (x,y) on the rectangular coordinate system can be represented by (r,θ) on the polar coordinate system, where r=x2+y2 and θ=arctan(yx)” is true or false.

Explanation

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

In the shown figure below:

Use Pythagorean theorem,

r2=x2+y2.

Thus, r=x2+y2.

Use the definition of trigonometric function,

tanθ=yx

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find more solutions based on key concepts 