% Newton method to solve for fi in assignment 1 of lab 1
h = 1;
fi = 0;
while abs(h) > 1.0e-10*abs(fi)
    f = 1.5*sin(fi) - (sin(fi))^3 - 0.64;
    fp = 1.5*cos(fi) - 3*(sin(fi))^2*cos(fi);
    h = f/fp;
    fi = fi - h;
end
format long
fi

% Presentation
fiv = 0:pi/200:pi/2;
x = (cos(fiv)).^3;
y = 1.5*sin(fiv) - (sin(fiv)).^3;
xf = inline('(cos(a))^3', 'a');
yf = inline('1.5*sin(a) - (sin(a))^3', 'a');
plot(x, y, xf(fi), yf(fi), '*')