Plot the points from the previous table and join them with a smooth curve.
Solution
Connecting the points with a smooth curve, we obtain the sketch shown.
When \(x = \dfrac{\pi}{2}\) and \(x = \dfrac{3 \pi}{2}\), \(\cos(x) = 0\) and \(\tan(x) = \dfrac{\sin(x)}{\cos(x)}\) are undefined.
Therefore, there are vertical asymptotes at \(x = \dfrac{\pi}{2}\) and \(x = \dfrac{3 \pi}{2}\). But what happens near the asymptotes? We will check values close to \(\dfrac{\pi}{2}\).