Question

If the point (x,square root 3/3) is on the unit circle, what is x?

Answer 1

recall the Unit circle has a radius of " 1 " thus \(\bf \begin{array}{llll}
(x&,&\frac{\sqrt{3}}{3})\\
\uparrow &&\uparrow \\
x&&y\\
\downarrow &&\downarrow \\
a&&b
\end{array}
\\ \quad \\
radius=1=c^2=a^2-b^2\implies c=\sqrt{a^2-b^2}\implies 1=\sqrt{x^2-\left(\frac{\sqrt{3}}{3}\right)^2}\)

Answer 2

Assume the center is (0,0). Unit circle has radius 1.
now substituting it in the equation x^2+y^2=r^2 gives the following
x^2=(1)^2-(sqrt 3/3)2
x^2= 1 - (3/9)
x^2 = 1-(1/3)
x^2 = 2/3
x = sqrt(2/3)
Is my answer correct???