Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Appendices - Section A.3 - Lines, Circles, and Parabolas - Exercises A.3 - Page AP-17: 3


The unit circle.

Work Step by Step

The LHS can be written as $(x-0)^{2}+(y-0)^{2}$, which is the square of the distance of the point $(x,y)$ from the origin, $(0,0)$. So, the distance of all these points from the origin is equal to the square root of the RHS, which is 1. This set of points is a circle, centered at the origin, with radius 1. We call this circle the unit circle. --- Alternatively, we could have compared the given equation to Equation (1) in the text $(x-h)^{2}+(y-k)^{2}=r^{2}$ the standard equation for a circle of radius $r,$ centered at $(h,k)$, and arrived to the same answer: the unit circle.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.