`cos((11 pi)/(6))=`

Options

A. `(1)/(2)`
B. `- (sqrt(3))/(2)`
C. 0
D. `(sqrt(3))/(2)`

Answer

To find the value of \( \cos\left(\frac{11\pi}{6}\right) \), we can follow these steps:

### Step 1: Rewrite the angle
We can express \( \frac{11\pi}{6} \) in a more manageable form. Notice that:
\[ \frac{11\pi}{6} = 2\pi - \frac{\pi}{6} \]
This means we can use the cosine identity for angles in the form of \( 2\pi - \theta \).

### Step 2: Apply the cosine identity
Using the identity \( \cos(2\pi - \theta) = \cos(\theta) \), we can simplify:
\[ \cos\left(\frac{11\pi}{6}\right) = \cos\left(2\pi - \frac{\pi}{6}\right) = \cos\left(\frac{\pi}{6}\right) \]

### Step 3: Find the cosine of \( \frac{\pi}{6} \)
We know that:
\[ \cos\left(\frac{\pi}{6}\right) = \cos(30^\circ) \]
From trigonometric values, we have:
\[ \cos(30^\circ) = \frac{\sqrt{3}}{2} \]

### Step 4: Conclusion
Thus, we find that:
\[ \cos\left(\frac{11\pi}{6}\right) = \frac{\sqrt{3}}{2} \]

### Final Answer
The value of \( \cos\left(\frac{11\pi}{6}\right) \) is \( \frac{\sqrt{3}}{2} \).

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