\( \left. \begin{array} { l } { \sin 60 ^ { \circ } = \sin \frac { \pi } { 3 } = } \\ { \cos 60 ^ { \circ } = \sin \frac { \pi } { 3 } } \\ { \Rightarrow \operatorname { tang } 60 ^ { \circ } = } \end{array} \right. \)

Did you know that the angle of \(60^\circ\) or \(\frac{\pi}{3}\) radians is one of the most famous in trigonometry? It appears frequently in equilateral triangles, where each angle measures \(60^\circ\). This means that in any equilateral triangle, all sides are equal, which leads to consistent sine and cosine values. For \(60^\circ\), \(\sin 60^\circ = \frac{\sqrt{3}}{2}\) and \(\cos 60^\circ = \frac{1}{2}\). Now, let's get down to the tangent function! Tangent is the ratio of sine to cosine, so for \(60^\circ\), you just divide \(\sin 60^\circ\) by \(\cos 60^\circ\). With the values provided, \( \tan 60^\circ = \frac{\sin 60^\circ}{\cos 60^\circ} = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}} = \sqrt{3} \). So, the tangent of \(60^\circ\) is \(\sqrt{3}\)!