Question

What is the distance between the following polar coordinates?: `(7,(5pi)/4), (2,(9pi)/8)`

Answer 1

`P_1P_2 = sqrt(53-28cos((pi)/8)) ~~5.209`

Explanation:

`P_1P_2 = sqrt(r_1^2+r_2^2-2r_1r_2cos(theta_2-theta_1))`
`r_1 = 7, theta_1 =(5pi)/4;r_2 =2, theta_2 =(9pi)/8`
`P_1P_2 = sqrt(7^2+2^2-2*7*2cos((9pi)/8-(5pi)/4))`
`P_1P_2 = sqrt(49+4-28cos(-(pi)/8)`
`P_1P_2 = sqrt(53-28cos((pi)/8)) ~~5.209`

Answer 2

`s~=5,27`

Explanation:

`r_1=7`
`r_2=2`
`theta_1=(5pi)/4`
`theta_2=(9pi)/8`
`theta_2-theta_1=(9pi)/8-(5pi)/4=(9pi-10pi)/8=-pi/8`

`cos(-pi/8)=0,9`

`s=sqrt(r_1^2+r_2^2-2*r_1*r_2*cos(theta_2-theta_1))`

`s=sqrt(7^2+2^2-2*7*2*0,9)`

`s=sqrt(49+4-28*0,9)`

`s=sqrt(53-25.2)`

`s=sqrt(27,8)`
`s~=5.27`