   Chapter 10.4, Problem 14E

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.(4, –2)

To determine

Two sets of polar coordinates for the point (4,2) and also plot the point.

Explanation

Given:

The cartesian coordinate, (4,2).

Formula used:

For the cartesian coordinate, (x,y), the polar coordinate is given by, (r,θ) or (r,π+θ) where r=x2+y2 and θ=tan1(yx).

Calculation:

Consider the cartesian coordinate, (4,2).

Here, x=4 and y=2 in the cartesian coordinate, (4,2).

Now, plot the point, (4,2) on a graph.

Assume the polar coordinate of (4,2), is given by, (r,θ).

Now, use the formula, r=x2+y2 to find r.

So,

r=42+(2)2=16+4=20=25

So, the distance from the origin is given by, 25

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