## 4.5-9
##
thetas = seq(0, 2*pi,, length.out=200)

obj_fn = function(x){
    45*cos(x)^2 - 18*cos(x)*sin(x) + 26*sin(x)^2
}

plot(thetas, sapply(thetas, obj_fn), 'l', col='blue')
grid()

theta_max = optimize(obj_fn, interval=c(2, 3), maximum=TRUE)
print(theta_max)
print(sqrt(theta_max$objective))