### Construct an Appropriate Triangle to Find the Missing ValuesTo solve trigonometric functions for different angles, we often construct right triangles. This can help us find the values of sine, cosine, and tangent functions for specific angles.#### Example: cos(30°)| Function | θ (deg) | θ (rad) | Function Value ||----------|---------|---------|---------------|| cos | 30° | ![pi/6](https://latex.codecogs.com/svg.latex?\pi/6) | |1. **Convert Degrees to Radians**: - For θ = 30°, we use the conversion \( \theta \text{ (rad)} = \theta \text{ (deg)} \times \frac{\pi}{180} \). - Therefore, θ = 30° is equivalent to \( \frac{\pi}{6} \) radians. This is confirmed by the green checkmark in the table.2. **Find the Cosine Function Value**: - The value for cos(30°) should be determined by constructing an appropriate right triangle or using the unit circle. - In a 30-60-90 triangle, the sides ratio is 1:√3:2. - The cosine of an angle is the adjacent side over the hypotenuse. Therefore, cos(30°) = √3 / 2.3. **Input the Function Value**: - The table has a space for inputting the function value adjacent to cos(30°) where the correct value of cos(30°) is √3 / 2. Notice the red cross indicating that the function value box is currently empty.### Important Notes- Degrees and radians are two units for measuring angles, where 180° = π radians.- Constructing triangles or using the unit circle can help verify trigonometric values. By practicing with various angles and constructing right triangles, you can become more comfortable with solving trigonometric functions.

Solution: The objective is to construct an appropriate triangle to find the missing values from the…

Answered: Construct an appropriate triangle to…

Construct an appropriate triangle to find the missing values. (0° ≤ 0 ≤ 90°, 0 ≤ 0 ≤ π/2) Function (deg) 0 (rad) Function Value cos X 30° TU 6

Trigonometry (MindTap Course List)

8th Edition

ISBN:9781305652224

Author:Charles P. McKeague, Mark D. Turner

Publisher:Charles P. McKeague, Mark D. Turner

Chapter2: Right Triangle Trigonometry

Section: Chapter Questions

Problem 1RP: The origins of the sine function are found in the tables of chords for a circle constructed by the...

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Question

### Construct an Appropriate Triangle to Find the Missing Values

To solve trigonometric functions for different angles, we often construct right triangles. This can help us find the values of sine, cosine, and tangent functions for specific angles.

#### Example: cos(30°)

| Function | θ (deg) | θ (rad) | Function Value |
|----------|---------|---------|---------------|
| cos | 30° | ![pi/6](https://latex.codecogs.com/svg.latex?\pi/6) | |

1. **Convert Degrees to Radians**:
- For θ = 30°, we use the conversion \( \theta \text{ (rad)} = \theta \text{ (deg)} \times \frac{\pi}{180} \).
- Therefore, θ = 30° is equivalent to \( \frac{\pi}{6} \) radians. This is confirmed by the green checkmark in the table.

2. **Find the Cosine Function Value**:
- The value for cos(30°) should be determined by constructing an appropriate right triangle or using the unit circle.
- In a 30-60-90 triangle, the sides ratio is 1:√3:2.
- The cosine of an angle is the adjacent side over the hypotenuse. Therefore, cos(30°) = √3 / 2.

3. **Input the Function Value**:
- The table has a space for inputting the function value adjacent to cos(30°) where the correct value of cos(30°) is √3 / 2. Notice the red cross indicating that the function value box is currently empty.

### Important Notes

- Degrees and radians are two units for measuring angles, where 180° = π radians.
- Constructing triangles or using the unit circle can help verify trigonometric values.

By practicing with various angles and constructing right triangles, you can become more comfortable with solving trigonometric functions.

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