Respuesta :
The answer to the question lays in the given equation Sin(θ - 30°) = ± Sin(θ + 30°), the relationship between the sine of an angle (θ) subtracted by 30 degrees and the sine of the same angle added by 30 degrees is explored.
1. The key concept to consider is the properties of the sine function:
- Sin(θ - 30°) means you are looking at the sine of an angle that is 30 degrees less than θ.
- Sin(θ + 30°) means you are looking at the sine of an angle that is 30 degrees more than θ.
2. The ± sign indicates that there are two possibilities for the relationship between Sin(θ - 30°) and Sin(θ + 30°):
- If the two angles are related by a symmetry property, the equation holds true.
- For example, Sin(60°) = Sin(90° - 30°) = Sin(90° + 30°) = Sin(120°), which shows a symmetrical relationship.
3. By understanding the symmetry properties of the sine function and considering the angle transformations involved (adding or subtracting 30 degrees), you can explore various values of θ where the equation Sin(θ - 30°) = ± Sin(θ + 30°) holds true.
Overall, this equation involves understanding the relationship between angles and the symmetry properties of the sine function to determine when the equation is satisfied.In the given equation Sin(θ - 30°) = ± Sin(θ + 30°), the relationship between the sine of an angle (θ) subtracted by 30 degrees and the sine of the same angle added by 30 degrees is explored.
1. The key concept to consider is the properties of the sine function:
- Sin(θ - 30°) means you are looking at the sine of an angle that is 30 degrees less than θ.
- Sin(θ + 30°) means you are looking at the sine of an angle that is 30 degrees more than θ.
2. The ± sign indicates that there are two possibilities for the relationship between Sin(θ - 30°) and Sin(θ + 30°):
- If the two angles are related by a symmetry property, the equation holds true.
- For example, Sin(60°) = Sin(90° - 30°) = Sin(90° + 30°) = Sin(120°), which shows a symmetrical relationship.
3. By understanding the symmetry properties of the sine function and considering the angle transformations involved (adding or subtracting 30 degrees), you can explore various values of θ where the equation Sin(θ - 30°) = ± Sin(θ + 30°) holds true.
Overall, this equation involves understanding the relationship between angles and the symmetry properties of the sine function to determine when the equation is satisfied.
