To find the reference angle for \( \frac{7\pi}{9} \), follow these steps:

### Step 1: Identify the Quadrant
Since \( \frac{7\pi}{9} \) is measured in radians, let's first determine its approximate location on the unit circle.

- Convert \( \frac{7\pi}{9} \) to degrees:
  \[
  \frac{7\pi}{9} \times \frac{180^\circ}{\pi} = \frac{7 \times 180^\circ}{9} = 140^\circ
  \]
This angle is in the second quadrant because it lies between \( 90^\circ \) and \( 180^\circ \).

### Step 2: Find the Reference Angle
In the second quadrant, the reference angle is found by subtracting the given angle from \( 180^\circ \). 

Thus:
\[
180^\circ - 140^\circ = 40^\circ
\]

Now, convert \( 40^\circ \) back to radians:
\[
40^\circ \times \frac{\pi}{180^\circ} = \frac{40\pi}{180} = \frac{2\pi}{9}
\]

### Final Answer:
The reference angle for \( \frac{7\pi}{9} \) is \( \frac{2\pi}{9} \) radians.

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you find reference angles in different quadrants?
2. What is the reference angle for \( \frac{8\pi}{9} \)?
3. Can reference angles ever be negative?
4. How does the unit circle relate to reference angles?
5. What is the reference angle for an angle greater than \( 2\pi \)?

**Tip:** Always remember that the reference angle is the smallest angle between the terminal side of the given angle and the x-axis.

Learn how to find the reference angle for 7π/9 in radians using simple steps. This trigonometry problem involves converting radians to degrees, identifying the quadrant, and applying the reference angle theorem. Ideal for students in Grades 9-12.

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