Question

Find the distance between (7, ) and(Show work)(5, ) on the polar plane.

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

point 1 (7 , 217/180 π)

point 2 (5 , - 23/36 π)

Step 02:

distance between points:

`d=\sqrt[]{r1^2+r2^2-2\cdot r1\cdot r2\cdot\cos \text{ (}\theta1-\theta2)}`

r1 = 7

r2 = 5

θ1 = 217/180 π

θ2 = - 23/36 π

`d=\sqrt[]{7^2+5^2-2\cdot7\cdot5\cdot\cos ((217)/(180)\pi-}(-(23)/(36)\pi))`

`d=\sqrt[]{49+25-70\cdot\cos (1.844\pi)}`

`d=\sqrt[]{4.3575}=2.0875`

The answer is:

distance = 2.0875