How to Find the Angle of a Curve

Sharp curves have high angles of inclination.
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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.

    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.

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

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

    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.

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