In the above picture, the point (√3/2, 1/2) is shown in blue, and the unit circle is shown in red.
By definition,
[tex]\tan (angle)=\frac{\text{ opposite side}}{\text{ adjacent side}}[/tex]
From the picture,
[tex]\begin{gathered} \tan (\theta)=\frac{\frac{1}{2}}{\frac{\sqrt[]{3}}{2}} \\ \tan (\theta)=\frac{1}{2}\cdot\frac{2}{\sqrt[]{3}} \\ \tan (\theta)=\frac{1}{\sqrt[]{3}} \\ \theta=\arctan (\frac{1}{\sqrt[]{3}}) \\ \theta=30^o \end{gathered}[/tex]
