Minimum vertical distance between graph of y=2+sinx and y=cosx is ?

1 Answer
Jul 30, 2018

Subtracting the second function from first we get the resultant function representing the variable vertical distance between the graphs with variation of x

So let it be

D(x)=2+sinx-cosx

=>D(x)=2+sqrt2(sinx*1/sqrt2-cosx*1/sqrt2)

=>D(x)=2+sqrt2(sinxcos(pi/4)-cosxsin(pi/4))

=>D(x)=2+sqrt2sin(x-pi/4)

D(x) will be minimum when sin(x-pi/4)=-1,the minimum value of sine function.

Hence

[D(x)]_"min"= 2-sqrt2