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The image contains a presentation slide on "Trigonometric Functions," specifically focusing on evaluating trigonometric functions exactly for special angle measures: \(30^\circ\), \(45^\circ\), and \(60^\circ\).

### Example:
The slide provides an example of evaluating trigonometric functions for a \(30^\circ\) angle. It illustrates a right triangle with the following labels:
- **Hypotenuse**: The side opposite the right angle.
- **Opposite**: The side opposite the \(30^\circ\) angle.
- **Adjacent**: The side adjacent to the \(30^\circ\) angle.

### Task:
The task is to evaluate the six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) for the angle \(30^\circ\).

### Solution:
Given the right triangle with angle \(30^\circ\):
- **Sin(30°) = Opposite/Hypotenuse = 1/2**
- **Cos(30°) = Adjacent/Hypotenuse = \(\sqrt{3}/2\)**
- **Tan(30°) = Opposite/Adjacent = 1/\(\sqrt{3}\)**

The reciprocals are:
- **Csc(30°) = 1/Sin(30°) = 2**
- **Sec(30°) = 1/Cos(30°) = 2/\(\sqrt{3}\)**
- **Cot(30°) = 1/Tan(30°) = \(\sqrt{3}\)**

Would you like any additional details or explanations? 

### 5 Related Questions:
1. How do you derive the exact values of trigonometric functions for a \(45^\circ\) angle?
2. What is the significance of special triangles in trigonometry?
3. Can you explain why the sine of \(30^\circ\) is \(1/2\)?
4. How do the trigonometric ratios change for an angle of \(60^\circ\)?
5. How can you use the unit circle to evaluate trigonometric functions for these special angles?

### Tip:
Remember that understanding the properties of the 30°-60°-90° triangle is key to quickly solving problems involving these specific angles in trigonometry.

Evaluating Trigonometric Functions Exactly for Special Angle Measures: 30°, 45°, and 60°. Example: Evaluating the six trigonometric functions for an angle that measures 30°.

Learn how to evaluate the trigonometric functions exactly for a 30° angle. This problem covers essential trigonometry concepts, including the sine, cosine, tangent, and their reciprocal functions. Suitable for high school students in Grades 9-12.

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