wht is the exact value of cos 11 pie over 6

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

1. **Convert the angle** \(\frac{11\pi}{6}\) into degrees:
   \[
   \frac{11\pi}{6} \times \frac{180^\circ}{\pi} = 330^\circ
   \]

2. **Determine the reference angle**: The reference angle for \(330^\circ\) is \(360^\circ - 330^\circ = 30^\circ\).

3. **Evaluate the cosine of the reference angle**: \(\cos(30^\circ) = \frac{\sqrt{3}}{2}\).

4. **Determine the sign** of the cosine in the fourth quadrant: Since \(330^\circ\) is in the fourth quadrant, where the cosine function is positive, \(\cos(330^\circ) = \frac{\sqrt{3}}{2}\).

So, the exact value of \(\cos\left(\frac{11\pi}{6}\right)\) is \(\frac{\sqrt{3}}{2}\).

Would you like any more details, or do you have any questions?

Here are some related questions:
1. What is the exact value of \(\sin\left(\frac{11\pi}{6}\right)\)?
2. How do you find the sine and cosine of an angle greater than \(2\pi\)?
3. What is the reference angle for \(\frac{13\pi}{6}\)?
4. How does the unit circle help in finding trigonometric values?
5. What are the signs of trigonometric functions in each quadrant?

**Tip:** Always consider the quadrant in which an angle lies when determining the sign of its trigonometric functions.

Learn how to find the exact value of cosine 11π/6 using trigonometric principles. Step-by-step solution includes converting the angle to degrees, determining the reference angle, and evaluating cosine in the appropriate quadrant. Suitable for high school students learning trigonometry.

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