How To Find The Angle Of A Curve

A curved line on a graph changes continuously in gradient. This means the rate of change of the y-axis's values changes constantly as the values of x change. The most common way for describing this gradient is a decimal value ranging from 0 to infinity. An alternate way of describing the slope is a line's angle of inclination. To find this vale for a curved line, you must draw a tangent, which is straight line, to the curve.

Step 1

Draw a straight line that touches the curve at a single point. This line must be equally close to the curve on either end of this contact point.

Step 2

Identify two points on this line. For example, two points might have coordinates of (2, 11) and (5, 35).

Step 3

Divide the difference between these points' y-coordinates by the difference between their x-coordinates. Continuing this example: (11 – 35) ÷ (2 – 5) = 8.

Step 4

Find the inverse tangent of this slope using a scientific calculator: tan-1 (8) = 82.9. This is the curve's inclination angle at the contact point.