21 Find the distance between the points with polar coordinat

21. Find the distance between the points with polar coordinates (2, 120°) and (1, 45°)

Solution

cartesian coordinates of (2, 120°)=(2cos120°,2sin120°)=(-1,3)

cartesian coordinates of (1, 45°)=(1cos45°,1sin45°)=(1/2 ,1/2)

distance between points =[(1/2 +1)²+(1/2 -3)²]

distance between points =[(1/2 +1+2)+(1/2 +3 -6)]

distance between points =[5+2 -6]

distance between points =1.9916