To find \( \cos\left(\frac{5\pi}{6}\right) \), let's go through the process step-by-step.

### Step 1: Determine the Reference Angle
The given angle is \( \frac{5\pi}{6} \). This angle is in the second quadrant of the unit circle. The reference angle for \( \frac{5\pi}{6} \) is:
\[
\pi - \frac{5\pi}{6} = \frac{\pi}{6}.
\]

### Step 2: Determine the Cosine of the Reference Angle
The cosine of the reference angle \( \frac{\pi}{6} \) is:
\[
\cos\left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{2}.
\]

### Step 3: Adjust the Sign Based on the Quadrant
Since \( \frac{5\pi}{6} \) is in the second quadrant, and the cosine is negative in the second quadrant, we have:
\[
\cos\left(\frac{5\pi}{6}\right) = -\frac{\sqrt{3}}{2}.
\]

Thus,
\[
\cos\left(\frac{5\pi}{6}\right) = -\frac{\sqrt{3}}{2}.
\]

Would you like more details or have any questions?

### Related Questions
1. What is the sine of \( \frac{5\pi}{6} \)?
2. How do you find the tangent of \( \frac{5\pi}{6} \)?
3. What are the circular function values for \( \frac{2\pi}{3} \)?
4. How do reference angles help in finding trigonometric values?
5. What are the properties of trigonometric functions in different quadrants?

### Tip
Always identify the reference angle and the quadrant when evaluating trigonometric functions to determine the correct sign and value.

Learn how to calculate cos(5π/6) step-by-step. This trigonometry problem explains how to determine the reference angle and find the cosine value for angles in the second quadrant. Suitable for students in Grades 10-12 studying trigonometric functions and the unit circle.

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