Find the principal values of sin⁻¹(-√3/2), cos⁻¹(-1/2) and tan⁻¹1/√3. Give each in radians.

Step 1. The inverse sine. $\sin\dfrac{\pi}{3} = \dfrac{\sqrt{3}}{2}$, and the sine is odd. So the angle is $-\dfrac{\pi}{3} = -1.0472$.

Step 2. The inverse cosine. $\cos\dfrac{\pi}{3} = \dfrac{1}{2}$. The cosine of $\pi - \dfrac{\pi}{3}$ is $-\dfrac{1}{2}$, and $\dfrac{2\pi}{3}$ lies in $[0, \pi]$. So the angle is $\dfrac{2\pi}{3} = 2.0944$.

Step 3. The inverse tangent. $\tan\dfrac{\pi}{6} = \dfrac{1}{\sqrt{3}}$, so the angle is $\dfrac{\pi}{6} = 0.5236$.