We have a unit circle (radius = 1).
Then we can relate the x and y coordinates to the angle θ as:
[tex]\begin{gathered} x=\cos (\theta) \\ y=\sin (\theta) \end{gathered}[/tex]
As the terminal point is (x,y)=((3^0.5)/2, 1/2), we can use any of these coordinates to find θ.
We will use y=1/2:
[tex]\begin{gathered} y=\sin (\theta)=\frac{1}{2} \\ \theta=\arcsin (\frac{1}{2}) \\ \theta=\frac{\pi}{6} \end{gathered}[/tex]
Answer: the angle θ is θ = π/6
NOTE: we could have obtained the same result with x:
[tex]\theta=\arccos (\sqrt[]{\frac{3}{2})}=\frac{\pi}{6}[/tex]
