The image shows a unit circle with a diagram labeled "3-point Extra Credit (in Progress category)" and a question that asks to "Express each number as non-fractional trig function of θ." There are labeled points on the diagram (4, 5, 6, etc.), and lines extending through various parts of the circle with different colors (e.g., red, green, purple lines).

Here's a possible breakdown of the problem:

1. The unit circle has a radius of 1.
2. The points labeled on the circle and lines probably correspond to specific angles and trigonometric values.
3. The goal is to express each number (e.g., 4, 5, 6) in terms of trigonometric functions, likely using standard values from the unit circle.

Strategy:

• Use the relationships between the x-coordinate, y-coordinate, and the trigonometric functions sine and cosine:
  • $\cos(\theta)$ gives the x-coordinate.
  • $\sin(\theta)$ gives the y-coordinate.
• Other functions such as tangent, secant, etc., may also be useful depending on how the lines relate to the unit circle.

Would you like a more detailed explanation or help expressing specific numbers (4, 5, 6) in terms of trigonometric functions of $\theta$? Feel free to ask for clarifications on any part of the problem.

Follow-up Questions:

1. Do you need help deriving the trigonometric expressions for each labeled point?
2. Should we calculate the specific angles corresponding to the points shown on the unit circle?
3. Would you like a refresher on unit circle properties, such as how angles relate to sine and cosine?
4. Is there a particular number (4, 5, 6) you'd like to start with in terms of finding its trigonometric expression?
5. Would you like a detailed breakdown of how non-fractional trigonometric functions are derived from the unit circle?

Tip:

The unit circle is a powerful tool for connecting geometric points with trigonometric functions like sine, cosine, and tangent. Always consider the coordinates of points on the circle!