Minimum vertical distance between graph of y=2+sinxandy=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+sinxcosx

D(x)=2+2(sinx12cosx12)

D(x)=2+2(sinxcos(π4)cosxsin(π4))

D(x)=2+2sin(xπ4)

D(x) will be minimum when sin(xπ4)=1,the minimum value of sine function.

Hence

[D(x)]min=22