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How do you use an angle and a line with tan to find the angle of a line to the x axis?
Wiki User
∙ 15y ago
The inclination of a line is the angle α, where 0° ≤ α < 180°, that is measured from the positive x-axis to the line.
Theorem: For any line with slope m and inclination α
m = tan α if α ≠ 90°.
If α ≠ 90°, then the line has no slope. (The line is vertical) In a coordinate system, draw a line L1 that passes through the origin and has inclination α. Let P be the point where L1 intersects the unit circle. Then P = (cos α, sin α). The slope of L1 is:
m = (sinα - 0)/(cos α - 0) = tan α.
If you draw another line line, L2, that has inclination α and does not contain the origin, it is parallel to L1. Therefore, the slope of L2 also equals tan α. As I understand, you are asking how to find the inclination angle when the equation of a line is given. For example, 2x + 3y = 14 Write the equation in the slope-intercept form;
y = - 2/3x + 14
slope = -2/3 = tan α α = arc tan (-2/3) = -33.7° (The reference angle is 33.7°)
Since tan α is negative and α is a positive angle, 90° < α < 180°.
The inclination is 180° - 33.7° = 146.3°.
Wiki User
∙ 15y ago
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