Question

What is the distance between the following polar coordinates?: `(12,(pi)/8), (-8,(5pi)/8)`

Answer 1

`color(crimson)("Distance " d ~~ 14.4222`

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 = 12, r_2 = -8, theta_1 = ((pi)/8)^c, theta_2 = ((5pi)/8)^c`

`d = sqrt (12^2 + -8^2 - (2 * 12 * -8 * cos ((5pi)/8 - (pi)/8))`

`color(crimson)(d )= sqrt (208 + cancel(192 cos (pi/2))) color(crimson)(~~ 14.4222), " as " cos (pi/2) = 0`