can you please sure the working out of getting 11pi/12

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 \(

Learn how to work with the angle \(\frac{11\pi}{12}\) in radians, including its conversion to degrees, determination of its quadrant in the unit circle, and calculation of its reference angle. This problem is suitable for advanced high school students studying trigonometry.

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