https://file.aiquickdraw.com/mathbot/file/1730403613459qtxk4t45.jpg

To solve this problem, let’s go through the information given and apply reasoning based on the unit circle.

### Problem Breakdown
1. The point \( p \) is located on the unit circle, which means the total circumference (or arc) around the circle is 1.
2. The arc from \( (1, 0) \) to \( p \) is given as \( \frac{8}{19} \) of the total circumference of the unit circle.
3. We are asked to find the fraction of the unit circle’s circumference for the arc going in the opposite direction—from \( p \) back to \( (1, 0) \).

### Solution
1. Since the total circumference is 1, the remaining arc (going from \( p \) to \( (1, 0) \)) must be the complement of \( \frac{8}{19} \).
   
2. This means the arc from \( p \) to \( (1, 0) \) will be:
   \[
   1 - \frac{8}{19} = \frac{19 - 8}{19} = \frac{11}{19}
   \]

### Conclusion
The fraction of the unit circle represented by the arc from \( p \) to \( (1, 0) \) is \( \frac{11}{19} \).

Would you like further details or explanations?

---

Here are some related questions to explore further:

1. What is the significance of arc length on a unit circle?
2. How can we determine the exact coordinates of point \( p \) based on this arc length?
3. How do we convert fractions of arc length to radians or degrees?
4. How can we use this concept in determining angles between points on a unit circle?
5. What other properties can be derived from fractional arcs on a unit circle?

**Tip:** In problems involving the unit circle, remembering that the entire circumference is \(2\pi\) (or 1 when normalized) can simplify calculations involving arc lengths and angles.

The point p is on the unit circle with the property that the arc from (1, 0) to p is 8/19 of the unit circle. Determine the fraction of the unit circle given by the arc from p to (1, 0).

Learn how to determine the fraction of a unit circle's circumference for an arc, given that the arc from (1, 0) to point p covers 8/19 of the circle. This problem uses unit circle properties and complementary arc length calculation, suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation