Question

What is the distance between the following polar coordinates?: `(11,(17pi)/12), (4,(pi)/8)`

Answer 1

`color(green)("Distance between the polar coordinates " ~~ 13.8047`

Explanation:

Distance between tow points knowing the polar coordinates is given by the formula using cosine rule

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

`"Given " r_1 = 11, r_2 = 4, theta_1 = ((17pi)/12)^c, theta_2 = ((pi)/8)^c`

`d = sqrt (11^2 +4^2 - (2 * 11 * 4* cos ((pi)/8 - (17pi)/12))`

`color(green)(d )= sqrt (137 - 88 cos ((-31pi)/24)) color(green)(~~ 13.8047)`