Let r represent an angle with a measure such that 0 degrees is less than r and less than 90 degrees.

Given that \( r \) represents an angle such that \( 0^\circ < r < 90^\circ \), this tells us that:

1. \( r \) is a positive angle.
2. The angle \( r \) is an acute angle because it is less than \( 90^\circ \).

In trigonometry, angles within this range have some important properties:

- **Sine and Cosine**: For \( 0^\circ < r < 90^\circ \), both \( \sin(r) \) and \( \cos(r) \) are positive.
- **Tangent and Cotangent**: The tangent function, \( \tan(r) = \frac{\sin(r)}{\cos(r)} \), is also positive in this range.
- **Reciprocal Functions**: The reciprocal functions, cosecant \( \csc(r) = \frac{1}{\sin(r)} \), secant \( \sec(r) = \frac{1}{\cos(r)} \), and cotangent \( \cot(r) = \frac{1}{\tan(r)} \), are all positive as well.

Would you like to explore more about trigonometric properties of acute angles or have any specific questions? 

### Relative Questions to Consider:
1. What are the values of sine, cosine, and tangent for specific angles like \( 30^\circ \), \( 45^\circ \), and \( 60^\circ \)?
2. How do the graphs of trigonometric functions look for angles between \( 0^\circ \) and \( 90^\circ \)?
3. Why are all trigonometric ratios positive in the first quadrant?
4. How are acute angles used in solving right triangle problems?
5. What are some real-life applications where acute angles are important?

### Tip:
Remember that knowing the properties of angles in different quadrants is crucial for solving trigonometric equations and understanding their behavior across the unit circle.

Explore the properties of acute angles and trigonometric functions like sine, cosine, and tangent for angles between 0° and 90°. This problem delves into key trigonometric formulas and theorems, suitable for high school students (Grades 9-12).

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