If \(\tan \phi<0\) and \(\sin \phi>0\), state the quadrant in which \(\phi\) lies.

Recall that in the coordinate plane, any angle can be represented in terms of its position relative to the four quadrants: - Quadrant I: All angles between \(0\) and \(90\) degrees (0 and \(\frac{\pi}{2}\) radians) - Quadrant II: All angles between \(90\) and \(180\) degrees (\(\frac{\pi}{2}\) and \(\pi\) radians) - Quadrant III: All angles between \(180\) and \(270\) degrees (\(\pi\) and \(\frac{3\pi}{2}\) radians) - Quadrant IV: All angles between \(270\) and \(360\) degrees (\(\frac{3\pi}{2}\) and \(2\pi\) radians) Trigonometric functions have specific signs depending on which quadrant they are: | Quadrant | sin | cos | tan | | ---------- | ----------- | ----------- | ----------- | | I | Positive | Positive | Positive | | II | Positive | Negative | Negative | | III | Negative | Negative | Positive | | IV | Negative | Positive | Negative | We are given that \(\tan \phi<0\) (Negative) and \(\sin \phi>0\) (Positive).

From the table above, we can see that the only quadrant where \(\tan \phi\) is negative and \(\sin \phi\) is positive is Quadrant II. Thus, the angle \(\phi\) lies in Quadrant II.