A line has direction cosines $\frac{\sqrt{3}}{2}, 0, -\frac{1}{2}$. What angles does it make with the $x$-, $y$- and $z$-axes?

Explanation

1. 01

   Each angle is the inverse cosine of its direction cosine: $\cos^{-1}\frac{\sqrt{3}}{2} = \frac{\pi}{6}$ and $\cos^{-1} 0 = \frac{\pi}{2}$.

2. 02

   $\cos^{-1}\left(-\frac{1}{2}\right) = \frac{2\pi}{3}$, an obtuse angle, because the cosine is negative.