For #f(t)= (sint,cost)# what is the distance between #f(pi/4)# and #f(pi)#?

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Answer 1 · 2017-01-14T07:32:41

Distance between #f(pi/4)# and #f(pi)# is #sqrt(2+sqrt2)#

This is a parametric form of equation.

At #f(pi/4)#, we have #f(pi/4)=(sin(pi/4),cos(pi/4))=(1/sqrt2,1/sqrt2)#

And at #f(pi)#, we have #f(pi)=(sinpi,cospi)=(0,-1)#

and distance between them is

#sqrt((0-1/sqrt2)^2+(-1-1/sqrt2)^2)#

#=sqrt(1/2+1+1/2+sqrt2)#

#=sqrt(2+sqrt2)#