Tangent and normal lines

You will write three functions: the tangent line to a curve at a point, the normal line at the same point, and the angle between two lines. A line is given as a pair (m, c) for $y = mx + c$. The checker tests several curves.

The idea. The gradient of the tangent is the derivative at the point. A computer can find it from a very short balanced interval, $\dfrac{f(x + h) - f(x - h)}{2h}$. The line has the point $(x_0, f(x_0))$ on it, so $c = f(x_0) - mx_0$. The normal has gradient $-\dfrac{1}{m}$. The angle between two lines with gradients $m_1$ and $m_2$ satisfies $\tan\varphi = \left|\dfrac{m_1 - m_2}{1 + m_1m_2}\right|$.

Your tasks.

1. Finish tangent_line(f, x0). Return (m, c), each rounded to 4 decimal places.
2. Finish normal_line(f, x0). Return (m, c) for the normal, rounded to 4 decimal places.
3. Finish angle_between(m1, m2). Return the acute angle in degrees, rounded to 2 decimal places.