| Interval | Sign of fs\(^\prime\) | Conclusion |
|---|---|---|
| \(\left( 0,\dfrac{\pi }{2}\right)\) | positive | \(f\) is increasing on \(\left( 0,\dfrac{\pi }{2}\right)\) |
| \(\left( \dfrac{\pi }{2},\dfrac{7\pi }{6}\right)\) | negative | \(f\) is decreasing on \(\left( \dfrac{\pi }{2},\dfrac{7\pi}{6}\right)\) |
| \(\left(\dfrac{7\pi}{6},\dfrac{3\pi}{2}\right)\) | positive | \(f\) is increasing on \(\left( \dfrac{7\pi }{6},\dfrac{3\pi}{2}\right)\) |
| \(\left( \dfrac{3\pi }{2},\dfrac{11\pi }{6}\right)\) | negative | \(f\) is decreasing on \(\left( \dfrac{3\pi }{2},\dfrac{11\pi }{6}\right)\) |
| \(\left( \dfrac{11\pi }{6},2\pi \right)\) | positive | \(f\) is increasing on \(\left( \dfrac{11\pi }{6},2\pi \right)\) |