The given angle is:

\[
\theta = \frac{7\pi}{6}
\]

This is an angle in radians. To understand this better, let's convert this into degrees and analyze it in the context of the unit circle.

1. **Converting to degrees**:
\[
\theta = \frac{7\pi}{6} \times \frac{180^\circ}{\pi} = \frac{7 \times 180^\circ}{6} = 210^\circ
\]
Thus, \(\theta = 210^\circ\).

2. **Position on the Unit Circle**:
An angle of \(210^\circ\) lies in the third quadrant of the unit circle.

3. **Reference Angle**:
The reference angle for \(210^\circ\) is:
\[
\text{Reference Angle} = 210^\circ - 180^\circ = 30^\circ
\]
This implies that \( \theta \) is \(30^\circ\) past \(180^\circ\), in the third quadrant.

4. **Sine and Cosine Values**:
For \( \theta = \frac{7\pi}{6} \):
- \( \sin(\theta) = -\sin(30^\circ) = -\frac{1}{2} \)
- \( \cos(\theta) = -\cos(30^\circ) = -\frac{\sqrt{3}}{2} \)

Would you like more details on the unit circle or any specific trigonometric functions related to this?

Here are 5 related questions you might explore:
1. What are the sine and cosine of other angles in the third quadrant?
2. How can we convert between radians and degrees more generally?
3. What is the tangent of \(\theta = \frac{7\pi}{6}\)?
4. How do the reference angles affect the trigonometric values?
5. How do we graph \(\theta = \frac{7\pi}{6}\) on the unit circle?

**Tip:** In the unit circle, angles measured counterclockwise from the positive x-axis are positive, while those measured clockwise are negative.

Explore how to solve the angle θ = (7π) / 6 in radians, converting it to degrees, understanding its position on the unit circle, and finding the sine and cosine values using reference angles. This problem is perfect for high school students in Grades 10-12 learning trigonometry.

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