How to Find the Angle of a Curve

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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.



About the Author

Ryan Menezes is a professional writer and blogger. He has a Bachelor of Science in journalism from Boston University and has written for the American Civil Liberties Union, the marketing firm InSegment and the project management service Assembla. He is also a member of Mensa and the American Parliamentary Debate Association.

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