Question

What is the distance between the following polar coordinates?: `(3,(5pi)/4), (1,(pi)/8)`

Answer 1

`color(chocolate)("Distance between the given two polar coordinates " d ~~ 3.94`

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 = 3, r_2 = 1, theta_1 = ((5pi)/4)^c, theta_2 = (pi/8)^c`

`d = sqrt (3^2 + 1^2 - (2 * 3 * 1 * cos (pi/8 - (5pi)/4))`

`color(chocolate)(d )= sqrt (10 - 6 cos ((-9pi)/8)) color(chocolate)(~~ 3.94`