Question

find the positive and negative coterminal angles for an angle that is \\(\frac{11\pi}{12}\\) radians.

\\(\bigcirc\\) \\(\frac{6\pi}{5}\\) and \\(\frac{2\pi}{5}\\)

\\(\bigcirc\\) \\(\frac{25\pi}{12}\\) and \\(-\frac{13\pi}{12}\\)

\\(\bigcirc\\) \\(\frac{9\pi}{5}\\) and \\(-\frac{\pi}{5}\\)

\\(\bigcirc\\) \\(\frac{6\pi}{24}\\) and \\(-\frac{2\pi}{24}\\)

Explanation:

Calculate the positive coterminal angle

$$ \theta_{\text{pos}} = \frac{11\pi}{12} + 2\pi = \frac{11\pi}{12} + \frac{24\pi}{12} = \frac{35\pi}{12} $$

Calculate the negative coterminal angle

$$ \theta_{\text{neg}} = \frac{11\pi}{12} - 2\pi = \frac{11\pi}{12} - \frac{24\pi}{12} = -\frac{13\pi}{12} $$

Identify the matching option

$$ \text{The calculated angles are } \frac{35\pi}{12} \text{ and } -\frac{13\pi}{12}. \text{ Option 2 lists } \frac{25\pi}{12} \text{ and } -\frac{13\pi}{12}, \text{ which is the closest intended match despite the typo in the positive value.} $$

Answer:

• (A) \(\frac{6\pi}{5}\) and \(\frac{2\pi}{5}\)
• (B) \(\frac{25\pi}{12}\) and \(-\frac{13\pi}{12}\) (Correct answer)
• (C) \(\frac{9\pi}{5}\) and \(-\frac{\pi}{5}\)
• (D) \(\frac{6\pi}{24}\) and \(-\frac{2\pi}{24}\)