Question

What is the distance between the following polar coordinates?: `(2,(3pi)/8), (-8,(5pi)/8)`

Answer 1

`color(orange)(" Distance " d = 9.5198`

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 = -8, theta_1 = ((3pi)/8)^c, theta_2 = ((5pi)/8)^c`

`d = sqrt (2^2 +-8^2 - (2 * 2 * -8* cos ((5pi)/8 - (3pi)/8))`

`color(orange)(d )= sqrt (68 + 32 cos ((pi)/4)) color(orange)(~~ 9.5198)`