Question

What is the distance between `(1 ,( pi)/4 )` and `(-1 , ( 3 pi )/2 )`?

Answer 1

`s=0,77" unit"`

Explanation:

`"use the formula :" s=sqrt(r_1^2+r_2^2-2*r_1*r_2*cos(theta_2-theta_1))`
`"the form of the polar coordinate:"`
`P_1=(r_1,theta_1)`
`P_2=(r_2,theta_2)`
`P_1=(1,pi/4)`
`P_2=(-1,(3pi)/2)`
`theta_2-theta_1=(3pi)/2-pi/4)=(5pi)/4`

`s=sqrt(1^2+(-1)^2+2*1*1*cos (5pi)/4)`

`s=sqrt(1+1+2*(-0,707)`
`s=sqrt(2-1,414)`
`s=sqrt(0,586)`
`s=0,77`