Math Problem Statement
Solution
The question asks you to select the formula for calculating the angle between two lines given in the plane by their general equations. In this context, the correct approach involves using the arctangent function with the appropriate combination of coefficients.
The general formula for the angle between two lines given by the equations and is:
Based on this formula, the correct answer is:
Option 2:
This option uses the arctangent (or "arctg" as written here) and matches the correct placement of the coefficients in the numerator and denominator.
Would you like further details or have any questions?
Here are some additional questions you may find useful to explore:
- How do you derive the angle formula for lines in the general form ?
- What is the meaning of each coefficient , , and in the line equation?
- How does the angle formula change for vertical or horizontal lines?
- Can this formula be applied to lines in three-dimensional space?
- What are some common applications of finding the angle between two lines?
Tip: When calculating angles between lines, always check if the lines are parallel (when the angle is or ) to simplify your solution.
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Math Problem Analysis
Mathematical Concepts
Analytic Geometry
Trigonometry
Formulas
Angle between two lines formula: \(\phi = \arctan \left( \frac{A_2B_1 - A_1B_2}{A_1A_2 + B_1B_2} \right)\)
Theorems
Formula for the angle between two lines
Suitable Grade Level
Grades 10-12
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