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 - Page 407: 8

Answer

Yes, ($\frac{\sqrt 11}{6},\frac{5}{6}$) is a point on the unit circle.

Work Step by Step

Since ($\frac{\sqrt 11}{6},\frac{5}{6}$) is an (x, y) coordinate we can plug it into the equation of a circle, $x^{2}+y^{2}=1$. $$(\frac{\sqrt 11}{6})^{2}+(\frac{5}{6})^{2}=1$$ $$\frac{\sqrt 11\times\sqrt 11}{6\times6}+\frac{5\times5}{6\times6}=1$$ $$\frac{11}{36}+\frac{25}{36}=1$$ $$\frac{36}{36}=1$$ We end up with 1=1, which is true. Therefore, ($\frac{\sqrt 11}{6},\frac{5}{6}$) is a point on the unit circle.
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