To work with the angle $\frac{11\pi}{12}$, we often need to determine its value in degrees, understand its placement on the unit circle, or perform trigonometric calculations. Let’s go through these steps systematically.

Step-by-Step Working for $\frac{11\pi}{12}$:

1. Convert $\frac{11\pi}{12}$ from Radians to Degrees:

   The formula to convert radians to degrees is: $\text{Degrees} = \text{Radians} \times \frac{180^\circ}{\pi}$

   Applying this formula to $\frac{11\pi}{12}$:

   $\frac{11\pi}{12} \times \frac{180^\circ}{\pi} = \frac{11 \times 180^\circ}{12}$

   $= \frac{1980^\circ}{12}$

   $= 165^\circ$

   So, $\frac{11\pi}{12}$ in degrees is $165^\circ$.

2. Determine the Quadrant of $165^\circ$:

   • $165^\circ$ is between $90^\circ$ and $180^\circ$.
   • Therefore, it lies in the second quadrant of the unit circle.

3. Understanding the Reference Angle:

   • The reference angle for an angle in the second quadrant is given by: $180^\circ - \text{angle}$

   • For (