SOLUTION: Find the distance between the points with polar coordinates (2, 2π/3) and (3, π/4).

Algebra ->  Trigonometry-basics -> SOLUTION: Find the distance between the points with polar coordinates (2, 2π/3) and (3, π/4).       Log On


   

Question 1022514: Find the distance between the points with polar coordinates (2, 2π/3) and (3, π/4).

Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
You use the law of cosines to find the distance, where a and b are the radial distances and the angle in the formula is the difference between them...here a = 2, b = 3, and theta = 2π/3 - π/4 = 5π/12
So we can write
c%5E2+=+a%5E2+%2B+b%5E2+-+2ab%2AcosC+=+2%5E2+%2B+3%5E2+-+2%282%29%283%29cos%285pi%2F12%29
and
c%5E2+=+13+-+12%2Acos%285pi%2F12%29
c%5E2+=+9.894
and
c = 3.1455