Question

What is the distance between the following polar coordinates?: `(2,(12pi)/8), (1,(-pi)/8)`

Answer 1

`color(purple)("Distance between the two polar coordinates " d )color(purple)(~~ 1.8626`

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 = 2, r_2 = 1, theta_1 = ((12pi)/8)^c, theta_2 = (-pi/8)^c`

`d = sqrt (2^2 + 1^2 - (2 * 2 * 1 * cos (-pi/8 - (12pi)/8))`

`color(purple)(d )= sqrt (5 - 4 cos ((-13pi)/8)) color(purple)(~~ 1.8626`