Is this point on the unit circle? I was working through my Precalculus 12 book, when I came across these questions:
Is each point on the unit circle? Give evidence to support your answer
a) $(0.65, -0.76)$
b) $\left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)$
My book says that both of these points lie on the unit circle, but I can't understand how.
 A: Hint:
A point with coordinates $(a,b)$ is in the unit circle if and only if
$$
a^2+b^2=1.
$$
Explanation: The unit circle is by definition a circle with radius equal to $1$ and center $(0,0)$, so the distance of the points $(x,y)$ in that circle to the center is equal to $1$, hence by the distance formula :
$$
\sqrt{a^2+b^2}=1\iff a^2+b^2=1.
$$
A: we have $x^2+y^2=1$ then we plug the coordinates in this equation
$$0.65^2+0.76^2=1.0001$$ and further
$$\left(\frac{\sqrt{2}}{2}\right)^2+\left(\frac{\sqrt{2}}{2}\right)^2=1/2+1/2=1$$
the second point is on the unit circle
A: If you are studying the unit circle, then b) should be a familiar cartesian coordinate, as it equivalent to the polar coordinate $\left(1,\frac{5\pi}{4}\right)$. To determine if a) is on the unit circle, you can do as others have suggested, and check the value of $$0.65^2+(-0.76)^2$$ If it equals $1$, it is on the unit circle. It does not equal $1$, which is easy to see by using a calculator. So technically that point is not on the unit circle, although the  value is so close to $1$ that it is reasonable to assume the book rounded the decimals. I would make a note of that if I were turning this in for homework.
