Find the principal value of \tan^{-1} (\sqrt{3})

Step 1: Take the given inverse trigonometric function
\tan^{-1} (\sqrt{3})
NOTE: \tan^{-1} \theta is defined as a function with values restricted to the range [math][0, \frac{\pi}{2}[/math])
Step 2: Determine the required angle of the function
Let \tan^{-1} (\sqrt{3}) = \theta
\tan \theta = \sqrt{3}
\tan \theta = \tan 60\degree
\theta = 60\degree ( \because A basic reference triangle looks like:
\tan \theta = \frac{opposite}{adjacent}
\tan 60\degree = \frac{\sqrt{3}}{1}