Home › NSC / Matric › Mathematics › Analytical Geometry › How is the gradient of a straight line related t…
How is the gradient of a straight line related to its angle of inclination?
AGradient is the sine of it
BGradient is the cosine of it
CGradient is the tangent of it
DGradient is the square of it
Answer & Solution
Correct answer: C. Gradient is the tangent of it
1. The angle of inclination is measured from the positive direction of the horizontal axis up to the line.
2. Drop a vertical from any point on the line to make a right angled triangle.
3. The rise is the side opposite the angle and the run is the side next to it.
4. Opposite divided by adjacent is the tangent, and rise divided by run is the gradient.
5. A negative gradient gives an obtuse angle, found by adding a straight angle to the negative result.
_Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 7: Analytical geometry_