Answer to Question #18415 in Calculus for freesia

Question

Find the point on the curve y = cos (x) closest to the point (1,1)

Answer 1

To the first we have to find function of distance:d=Sqrt((x-x0)^2+(y-y0)^2)
For our function: d(x)=Sqrt((x-1)^2+(cos(x)-1)^2)
Let's derive it:((x-1)-sin(x)(cos(x)-1))/Sqrt((x-1)^2+(cos(x)-1)^2))
It will be zero (minimum) at point when next equality istrue: x-1=sinx(cosx-1)
It's a transcendent equation that can be solved onlynumerical: x=0.8
So, cos(x)=0.69.
It's a point (0.8,0.69)