Find the exact value of \( \cos \frac{11 \pi}{6} \)

Did you know that the angle \( \frac{11\pi}{6} \) radians is equivalent to \( 330^\circ \)? This angle is located in the fourth quadrant of the unit circle, where cosine values are positive. The reference angle for \( 330^\circ \) is \( 360^\circ - 330^\circ = 30^\circ \), which corresponds to \( \frac{\pi}{6} \) radians. Therefore, \( \cos \frac{11\pi}{6} = \cos \frac{\pi}{6} = \frac{\sqrt{3}}{2} \). To visualize this on the unit circle, you can plot the angle \( \frac{11\pi}{6} \) and see that it wraps around almost a full revolution. Since cosine represents the x-coordinate in the unit circle, the value at this angle indeed confirms that \( \cos \frac{11\pi}{6} = \frac{\sqrt{3}}{2} \). Don’t forget, understanding the unit circle is a key concept for mastering trigonometry!