## Precalculus: Mathematics for Calculus, 7th Edition

Yes, ($\frac{3}{5},-\frac{4}{5}$) is a point on the unit circle.
Since ($\frac{3}{5},-\frac{4}{5}$) is an (x, y) coordinate we can plug it into the equation of a circle, $x^{2}+y^{2}=1$. $$(\frac{3}{5})^{2}+(-\frac{4}{5})^{2}=1$$ $$\frac{3\times3}{5\times5}+\frac{-4\times-4}{5\times5}=1$$ $$\frac{9}{25}+\frac{16}{25}=1$$ $$\frac{25}{25}=1$$ We end up with 1=1, which is true. Therefore, ($\frac{3}{5},-\frac{4}{5}$) is a point on the unit circle.