Question

What is the distance between `(2 ,(7 pi)/6 )` and `(2 , (5 pi )/12 )`?

Answer 1

`s=3,695" unit"`

Explanation:

`" distance between two point which given at polar form:"`
`s=sqrt(r_1^2+r_2^2-2*r_1*r_2*cos(theta_2-theta_1))`
`P_1=(r_1,theta_1)" Point "P_1`
`P_2=(r_2,theta_2)" Point "P_2`
`P_1=(2,(7pi)/6)`
`P_2=(2,(5pi)/12)`
`r_1=2`
`r_2=2`
`theta_1=(7pi)/6`
`theta_2=(5pi)/12`

`theta_2-theta_1=(5pi)/12-(7pi)/6`
`theta_2-theta_1=(5pi-14pi)/12`

`theta_2-theta_1=-(9pi)/12`
`cos(-(9pi)/12)=-0,707`
`s=sqrt(2^2+2^2-2*2*2*(-0,707))`
`s=sqrt(4+4+8*0,707`
`s=sqrt(8+5,656)`
`s=sqrt(13,656)`
`s=3,695" unit"`