Question

Convert the equation to polar form. $$ y=5 $$

   Convert the equation to polar form.
$$
y=5
$$

Algebra and Trigonometry

Algebra and Trigonometry

James Stewart,… 3rd Edition

Chapter 9, Problem 46

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Solved by Expert Joseph Lentino

07/30/2020

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Convert the equation to polar form. $$ y=5 $$

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Key Concepts

Cartesian and Polar Coordinate Systems

This concept involves understanding the difference between the Cartesian coordinate system, which represents points as (x, y), and the polar coordinate system, which represents points as (r, ?). Recognizing how each system describes locations in the plane is crucial for converting equations from one form to the other.

Substitution of Coordinate Relationships

In converting equations from Cartesian to polar form, the key step is substituting the relationships x = r cos ? and y = r sin ? into the original Cartesian equation. This substitution directly transforms the equation into one that involves the polar variables r and ?.

Polar Equation Representation

Once the substitution is complete, the equation is expressed entirely in terms of r and ?. This new form, called the polar form, often reveals geometrical properties of the curve or line that might not be apparent in Cartesian form.

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