https://file.aiquickdraw.com/mathbot/file/1728649694120yfw3ywjk.pdf

The document appears to contain a set of mathematical questions related to trigonometry and geometry. Below are the main questions extracted from the document:

1. **Trigonometric Functions on the Unit Circle**:
   - A point \( A \) on the unit circle is given after one revolution. The task is to:
     - Calculate all 6 trigonometric functions (sine, cosine, tangent, cotangent, secant, cosecant) for this point.
     - Identify the quadrant where the point lies.
     - Find the reference angle with respect to the X-axis.

2. **Alice's Geometry Problem**:
   - Alice observes an object on top of a 6-meter-high tree from two points, A (4 meters from the tree) and B (2 meters closer).
     - Find the angles formed by Alice at points A and B relative to the tree's top.
     - Compare the angles and draw a conclusion.
     - Calculate the distances from Alice to the object at both points.

3. **Trigonometric Equations**:
   - Write a trigonometric equation and find its stretching factor, period, phase shift, vertical asymptotes, and domain.
   - Plot and analyze a sine or cosine graph by identifying specific points.

4. **Graphing Trigonometric Functions**:
   - Fill out a table for a preferred trigonometric function and its inverse.
   - Discuss periodicity, domain, range, and whether the function is even, odd, or neither.

Would you like assistance with any specific part of this? I can start solving one of these or provide detailed explanations. Let me know how you’d like to proceed!

### Expansion questions:
1. How are the trigonometric functions derived from coordinates on the unit circle?
2. What method would you use to find the angles formed by Alice at points A and B?
3. How can we analyze the phase shift and period of a trigonometric equation?
4. What are the properties of inverse trigonometric functions in terms of domain and range?
5. What distinguishes even, odd, and neither functions?

**Tip**: When analyzing angles in a real-world context, the tangent function is often helpful for comparing heights and distances directly.

The document contains a set of mathematical problems related to trigonometry and geometry, including calculating trigonometric functions on the unit circle, solving a real-world geometry problem, and analyzing trigonometric equations.

Explore trigonometric functions on the unit circle, solve real-world geometry problems involving angles and distances, and analyze trigonometric equations with sine and cosine functions. This guide covers key concepts in trigonometry and geometry, perfect for high school students.

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