Precisely calculate the angle between two curves where they intersect. Our Angle Between Two Curves Calculator simplifies this calculus concept, allowing you to input the tangent line slopes (derivatives) at the intersection point to find the angle in both degrees and radians. Perfect for academic use and quick checks of your calculus homework.
Formula:
The angle θ between two curves at their intersection point is determined by the angle between their respective tangent lines at that point. If the slopes of the tangent lines are m1 and m2, the formula is:
tan(θ) = |(m1 - m2) / (1 + m1m2)|
From this, the angle θ can be found using the inverse tangent function (arctan):
θ = arctan(|(m1 - m2) / (1 + m1m2)|)
Note: If 1 + m1m2 = 0, the lines are perpendicular, and θ = 90° (π/2 radians).