   Chapter 10.4, Problem 15E

Chapter
Section
Textbook Problem

# Rectangular-to-Polar Conversion In Exercises 11–20, the rectangular coordinates of a point are given. Plot the point and find two sets of polar coordinates for the point for 0 ≤ θ < 2π. ( − 1 , − 3 )

To determine

To calculate: Two sets of polar coordinates for the point (1,3) for 0θ<2π and plot the point (1,3) in rectangular coordinates.

Explanation

Given:

The provided rectangular coordinates are:

(1,3)

The interval is provided to be 0θ<2π.

Formula used:

The polar coordinates (r,θ) of a point are related to the rectangular coordinates (x,y) of the point as follows:

tanθ=yxr2=x2+y2

Calculation:

Consider the provided rectangular point (1,3).

Plot this point on a rectangular graph as shown below:

Now, the polar coordinates (r,θ) of a point are related to the rectangular coordinates (x,y) of the point as follows:

tanθ=yx …… (1)

r2=x2+y2 …… (2)

Thus, substitute 3 for y and

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