Question

What is the distance between the following polar coordinates?: `(2,(7pi)/12), (1,(2pi)/12)`

Answer 1

`P_1P_2=sqrt(3.96472382) ~~1.99`

Explanation:

Distance Formula in Polar Plane: `P_1P_2=sqrt(r_1^2+r_2^2-2r_1r_2cos(theta_2-theta_1))`

`r_1=2, theta_1=(7pi)/12, r_2=1,theta_2=(2pi)/12`

`P_1P_2=sqrt(2^2+1^2-2(2)(1)cos((2pi)/12-(7pi)/12))`

`P_1P_2=sqrt(4+1-4cos(-(5pi)/12))`

`P_1P_2=sqrt(5-4cos((5pi)/12))`

`P_1P_2=sqrt(3.96472382) ~~1.99`