how can i calculate the angle of each gradient and x axis?

i have a line, its a sigmoid function. the code is like this

x = 0:0.1:10;
y = sigmf(x,[2 4]);
plot(x,y)
xlabel('sigmf, P = [2 4]')
ylim([-0.05 1.05])

i want to know every angle between each pair of point and the x axis. i mean for line y of x=0 and x=0.1, the angle is..

for line y of x=0.1 and x=0.2 the angle is...

how can i calculate that? thank you before!

Answer 1

[David Wilson]

You could always differentiate to get the slope and then take the arc-tan.

syms x real 
s = 1/(1 + exp(-2*(x-4)))
dsdx = diff(s,x) % lazy way to get derivative 
slope = matlabFunction(dsdx)

x = [0:0.1:10]';
y = sigmf(x,[2 4]);
Angle = atan2d(slope(x),1) % note degrees 

subplot(2,1,1);
plot(x,y,'o-')
subplot(2,1,2);
plot(x, Angle); ylabel('angle [deg]')

[Yana Muhamadinah]

thanks a lot!