Draw an angle for two functions

Hello together,

I want to draw the angles between the X-Axis an my functions as shown in the picture.

How do I do this?

f = @(x) (tan((31.157/180) * pi) * x) - ((9.81*x.^2)/(2*25*25*(cos((31.157/180)*pi))^2));

g = @(x) (tan((62.774/180) * pi) * x) - ((9.81*x.^2)/(2*25*25*cos(((62.774/180)*pi))^2));

x = 0:0.1:60;

grid on;

hold on;

plot(x, f(x));

plot(x, g(x));

Answer 1

[Takumi]

I think there are other better ways...

f = @(x) (tan((31.157/180) * pi) * x) - ((9.81*x.^2)/(2*25*25*(cos((31.157/180)*pi))^2));
g = @(x) (tan((62.774/180) * pi) * x) - ((9.81*x.^2)/(2*25*25*cos(((62.774/180)*pi))^2));

% tangent gradient at origin
syms x
df = matlabFunction( diff(f(x)) );
dg = matlabFunction( diff(g(x)) );
alpha = atan(df(0));
beta = atan(dg(0));

x = 0:0.1:60;
plot(x, f(x));
grid on;hold on;axis equal
plot(x, g(x));
% plot(x,df(0)*x);    % tangent line
% plot(x,dg(0)*x);

% circular arc
% alpha
xIntF = 5;  % X-coordinate of the intersection of circle and f(x)
yIntF = f(xIntF);
rIntF = sqrt(xIntF^2+yIntF^2);    % radius for alpha
theta = linspace(0,atan(yIntF/xIntF),100);
xalpha = rIntF*cos(theta);
yalpha = rIntF*sin(theta);
plot(xalpha,yalpha,'-k');
xt = 6; yt = 1; % text location
str = sprintf('\\alpha=%2.1f°',alpha*180/pi);
text(xt,yt,str)

% beta
xIntG = 6;  % X-coordinate of the intersection of circle and g(x)
yIntG = g(xIntG);
rIntG = sqrt(xIntG^2+yIntG^2);    % radius for beta
theta = linspace(0,atan(yIntG/xIntG),100);
xbeta = rIntG*cos(theta);
ybeta = rIntG*sin(theta);
plot(xbeta,ybeta,'-k');
xt = 13; yt = 1; % text location
str = sprintf('\\beta=%2.1f°',beta*180/pi);
text(xt,yt,str)

[Max Brückner]

Thank you. That's exactly what I looked for.