How to Find the Angle of a Curve

Sharp curves have high angles of inclination.
••• Jupiterimages/Polka Dot/Getty Images

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.

Related Articles

How to Calculate the Slope of Regression Line
How to Calculate Slope Ratio
How to Find The Slope of a Line Given Two Points
How to Divide Rational Numbers
How to Work Out a Gradient of a Curve
How to Calculate Regression Coefficient
How to Convert Graphs to Equations
How to Straighten an Inverse Curve
How to Determine the Y-Intercept of a Trend Line
How to Find the Slope of a Nonlinear Line
How to Find Equations of Tangent Lines
How to Calculate the Slope of a Line of Best Fit
How to Find the X Intercept of a Function
How to Find a Parallel Line
How to Figure Out the Slope of a Line
How to Find the Slope in a Circle
How to Find Y Value for the Slope of a Line
How to Create Linear Equations
How to Solve a Parabola
How to Calculate Logit

Dont Go!

We Have More Great Sciencing Articles!