Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 5 - Secton 5.1 - The Unit Circle - 5.1 Exercises: 4


Yes, ($-\frac{24}{25},-\frac{7}{25}$) is a point on the unit circle.

Work Step by Step

Since ($-\frac{24}{25},-\frac{7}{25}$) is an (x, y) coordinate we can plug it into the equation of a circle, $x^{2}+y^{2}=1$. $$(-\frac{24}{25})^{2}+(-\frac{7}{25})^{2}=1$$ $$\frac{-24\times-24}{25\times25}+\frac{-7\times-7}{25\times25}=1$$ $$\frac{576}{625}+\frac{49}{625}=1$$ $$\frac{625}{625}=1$$ We end up with 1=1, which is true. Therefore, ($-\frac{24}{25},-\frac{7}{25}$) is a point on the unit circle.
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