Question
determine the sign of sin (5pie/4) and the quadrant in which it lies
And is it negative or positive
And is it negative or positive
Answers
GPT-4o mini
To determine the sign of \(\sin\left(\frac{5\pi}{4}\right)\) and the quadrant in which it lies, we can follow these steps:
1. **Identify the angle:** \(\frac{5\pi}{4}\) radians is equivalent to \(225^\circ\).
2. **Determine the quadrant:** Angles between \(180^\circ\) and \(270^\circ\) (or between \(\pi\) and \(\frac{3\pi}{2}\) radians) lie in the third quadrant. Therefore, \(\frac{5\pi}{4}\) is in the third quadrant.
3. **Determine the sign of \(\sin\) in the third quadrant:** In the third quadrant, the sine function is negative.
Thus, \(\sin\left(\frac{5\pi}{4}\right)\) is **negative**, and it lies in the **third quadrant**.
1. **Identify the angle:** \(\frac{5\pi}{4}\) radians is equivalent to \(225^\circ\).
2. **Determine the quadrant:** Angles between \(180^\circ\) and \(270^\circ\) (or between \(\pi\) and \(\frac{3\pi}{2}\) radians) lie in the third quadrant. Therefore, \(\frac{5\pi}{4}\) is in the third quadrant.
3. **Determine the sign of \(\sin\) in the third quadrant:** In the third quadrant, the sine function is negative.
Thus, \(\sin\left(\frac{5\pi}{4}\right)\) is **negative**, and it lies in the **third quadrant**.