Find tan 1230°, exactly and as a decimal to 3 places.

Step 1. Whole turns. $1230^\circ = 3 \times 360^\circ + 150^\circ$.

Step 2. The quadrant. $150^\circ$ is in quadrant II, and its acute angle with the x-axis is $30^\circ$.

Step 3. The value. $\tan 150^\circ = -\tan 30^\circ = -\dfrac{1}{\sqrt{3}} \approx -0.577$.