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

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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.