Sure! Let's express the solutions in radians in exact form, based on the general solution.

### Step 1: Recall the general solutions for \( x \).

We found the general solutions:

\[
x = \frac{5\pi}{3} + 4k\pi \quad \text{and} \quad x = \frac{7\pi}{3} + 4k\pi
\]

### Step 2: Substitute integer values for \( k \) to get solutions within the interval \( [0, 27) \).

#### For \( x = \frac{5\pi}{3} + 4k\pi \):

- When \( k = 0 \): 
  \[
  x = \frac{5\pi}{3}
  \]
- When \( k = 1 \):
  \[
  x = \frac{5\pi}{3} + 4\pi = \frac{5\pi}{3} + \frac{12\pi}{3} = \frac{17\pi}{3}
  \]

#### For \( x = \frac{7\pi}{3} + 4k\pi \):

- When \( k = 0 \):
  \[
  x = \frac{7\pi}{3}
  \]
- When \( k = 1 \):
  \[
  x = \frac{7\pi}{3} + 4\pi = \frac{7\pi}{3} + \frac{12\pi}{3} = \frac{19\pi}{3}
  \]

### Final Exact Solutions in Radians:
The exact solutions in the interval \( [0, 27) \) in radians are:

\[
x = \frac{5\pi}{3}, \frac{7\pi}{3}, \frac{17\pi}{3}, \frac{19\pi}{3}
\]

Let me know if you'd like further clarification or details on any step!

Here are 5 related questions to consider:
1. What is the significance of using exact values in trigonometry?
2. How do you identify all possible solutions for trigonometric equations within a specific interval?
3. How can you determine the general solution for a cosine equation?
4. Why do we add multiples of the period when solving trigonometric equations?
5. How do radian measures relate to the unit circle?

**Tip:** When dealing with exact trigonometric values, expressing your solutions in terms of \( \pi \) often preserves accuracy and simplifies further calculations.

Learn how to express trigonometric solutions in exact radians. This problem involves solving trigonometric equations and expressing the solutions accurately in radians. Suitable for Grades 11-12.

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