Question

Find the distance between the points A(Cos x , Sin x) and B(Sin x , -Cos x).​

Answer 1

Answer:

$\sqrt{2}$

Step-by-step explanation:

distance between 2 points (x1,y1) and (x2,y2) is$\sqrt{(x2-x1)^{2} + (y2-y1)^{2} }$

here x1 is cosx and y1 is sinx

x2 is sinx and y2bis -cosx

$(x2-x1)^{2}$ = $(sinx-cosx)^{2}$ =$(sinx)^{2}$ + $(cosx)^{2}$-2sinx.cosx

$(y2-y1)^{2}$ = $(-(sinx+cosx))^{2}$ = $(sinx)^{2}$ + $(cosx)^{2}$ + 2sinx.cosx

adding both terms we get 2( $(sinx)^{2}$ + $(cosx)^{2}$ ) = 2  [since $(sinx)^{2}$ + $(cosx)^{2}$ =1]

so answer is square root of 2.