Question

Which angle has its terminal side in the third quadrant?

(1 point)
Responses

Start Fraction 3 pi over 4 End Fraction
Image with alt text: Start Fraction 3 pi over 4 End Fraction

Start Fraction pi over 3 End Fraction
Image with alt text: Start Fraction pi over 3 End Fraction

Start Fraction 5 pi over 3 End Fraction
Image with alt text: Start Fraction 5 pi over 3 End Fraction

Start Fraction 7 pi over 6 End Fraction
Image with alt text: Start Fraction 7 pi over 6 End Fraction

Answer 1

To determine which angle has its terminal side in the third quadrant, we need to know the ranges for angles in standard position:

- The angles in the third quadrant are between \(\pi\) and \(\frac{3\pi}{2}\) (or between 180 degrees and 270 degrees).

Now let's evaluate each of the given angles:

1. \(\frac{3\pi}{4}\): This is in the second quadrant (between \(\frac{\pi}{2}\) and \(\pi\)).
2. \(\frac{\pi}{3}\): This is in the first quadrant (between \(0\) and \(\frac{\pi}{2}\)).
3. \(\frac{5\pi}{3}\): This is in the fourth quadrant (between \(\frac{3\pi}{2}\) and \(2\pi\)).
4. \(\frac{7\pi}{6}\): This is in the third quadrant (between \(\pi\) and \(\frac{3\pi}{2}\)).

Therefore, the angle that has its terminal side in the third quadrant is:

**\(\frac{7\pi}{6}\)**.