From the given figure
The radius of the circle is OC
Its length = the x-coordinate of point (1, 0), then
OC = 1
Let the x-coordinate of point C is x and the y-coordinate of it is y
We will use the trigonometry ratios to find x and y
Since the angle opposite to y and adjacent to x is 30 degrees, then
[tex]\begin{gathered} \cos 30=\frac{x}{OC}=\frac{x}{1} \\ \cos 30=x \end{gathered}[/tex]Since cos 30 = root3/2
[tex]x=\frac{\sqrt[]{3}}{2}[/tex][tex]\begin{gathered} \sin 30=\frac{y}{OC}=\frac{y}{1}=y \\ \cos 30=\frac{1}{2} \end{gathered}[/tex]Then
[tex]y=\frac{1}{2}[/tex]The coordinates of point C are
[tex](\frac{\sqrt[]{3}}{2},\frac{1}{2})[/tex]