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To solve \( \cos \left( \frac{\pi}{6} \right) \) using the unit circle provided in the image:

1. The unit circle represents the cosine and sine values for standard angles, with the x-coordinate corresponding to the cosine of the angle and the y-coordinate to the sine of the angle.
2. \( \frac{\pi}{6} \) radians is one of the key angles, and it corresponds to 30 degrees.
3. On the unit circle, the coordinates for \( \frac{\pi}{6} \) are \( \left( \frac{\sqrt{3}}{2}, \frac{1}{2} \right) \).
4. Since cosine corresponds to the x-coordinate, we have:
   \[
   \cos \left( \frac{\pi}{6} \right) = \frac{\sqrt{3}}{2}
   \]

Thus, \( \cos \left( \frac{\pi}{6} \right) = \frac{\sqrt{3}}{2} \).

Would you like further details on this, or do you have any questions?

Here are 5 related questions you can try:
1. What is \( \sin \left( \frac{\pi}{6} \right) \)?
2. Find \( \cos \left( \frac{\pi}{4} \right) \) using the unit circle.
3. What is the value of \( \cos \left( \frac{\pi}{3} \right) \)?
4. Can you compute \( \tan \left( \frac{\pi}{6} \right) \)?
5. How do you calculate \( \sin \left( \frac{5\pi}{6} \right) \) using the unit circle?

**Tip**: On the unit circle, the cosine values mirror symmetrically across the y-axis, and sine values mirror across the x-axis!

Use the (x,y) coordinates in the figure to find the value of the trigonometric function at the indicated real number, t, or state that the expression is undefined. Find cos(π/6).

Learn how to find the cosine of π/6 using the unit circle. This trigonometry problem involves key concepts such as radians, coordinates on the unit circle, and understanding cosine as the x-coordinate. Suitable for high school students in Grades 9-12.

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