DISTANCE BETWEEN TWO POLAR COORDINATES

To find the distance between two polar coordinates given by r and θ, we use the formula given below.

Find the distance between two polar coordinates.

Problem 1 :

(2, π/3) and (2, 11π/6)

Solution :

From the given points, we know that

r1 = 2, r2 = 2, 𝜃1 = π/3, 𝜃2 = 11π/6

Problem 2 :

(4, 7π/12) and (2, π/12)

Solution :

From the given points, we know that

r1 = 4, r2 = 2, 𝜃1 = 7π/12, 𝜃2 = π/12

Problem 3 :

An air traffic controller's radar display uses polar coordinates. A passing plane is detected at 285° counter-clockwise from north at a distance of 3 miles from the radar. Thirty seconds later the plane is detected at 225° and 2 miles. Estimate the plane's speed in miles per hour.

Solution :

Writing the points as (r, 𝜃), we get

(3, 285°) and (2, 225°)

d = 2.645 miles

Time taken to cover the distance = 30 seconds

1 hour = 60 minutes

1 minute = 60 seconds

30 seconds = 30/(60 x 60)

= 1/120 hour

= 1/120

Speed = distance / time

= 2.645 / (1/120)

= 120 (2.645)

= 317.4 miles per hour.

Problem 4 :

(2, π/6) and (4, π/3)

Solution :

From the given points, we know that

r1 = 2, r2 = 4, 𝜃1 = π/6, 𝜃2 = π/3

= 4.383

Problem 5 :

(3, 7π/4) and (1, π/4)

Solution :

From the given points, we know that

r1 = 3, r2 = 1, 𝜃1 = 7π/4, 𝜃2 = π/4

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