Find tan⁻¹5 + tan⁻¹1/2, then tan⁻¹(-5) + tan⁻¹(-1/2), then tan⁻¹5 + tan⁻¹1/5. Give each in radians.

Step 1. The first sum. $xy = \dfrac{5}{2} > 1$ and $x > 0$. The fraction is $\dfrac{5.5}{1 - 2.5} = -\dfrac{11}{3}$. So the sum is $\pi + \tan^{-1}\left(-\dfrac{11}{3}\right) = 3.1416 - 1.3046 = 1.8370$.

Step 2. The second sum. Both numbers are negative, so the sum is the negative of the first: $-1.8370$. The rule gives $-\pi + \tan^{-1}\dfrac{11}{3} = -3.1416 + 1.3046$.

Step 3. The third sum. $xy = 1$ and $x > 0$, so the sum is $\dfrac{\pi}{2} = 1.5708$.