Angle of intersection
When the graphs intersect with two functions, the tangents form two angles with each other. The smaller angle is called the angle of intersection.
The picture: By cutting the two tangents (red) two angles are formed: $\gamma$ and $\gamma'$.
$\gamma$ is the angle of intersection.
First, you need the slope angles of the functions:
The angle of intersection has the smaller value:
What is the angle of intersection of the functions $f(x)=x^2$ and $g(x)=x+2$ at the intersection $P(2|4)$.
Calculate slopesThe slope of the two functions at the intersection is calculated ($x=2$).
Calculate slope angle$\alpha=\arctan(f'(x))$
Specify the angle of intersection$\gamma_1=|\alpha-\beta|$
=> The angle of intersection $\gamma$ is $30.96°$