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
r_{1} = 2, r_{2} = 2, 𝜃_{1} = π/3, 𝜃_{2} = 11π/6
Problem 2 :
(4, 7π/12) and (2, π/12)
Solution :
From the given points, we know that
r_{1} = 4, r_{2} = 2, 𝜃_{1} = 7π/12, 𝜃_{2} = 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
r_{1} = 2, r_{2} = 4, 𝜃_{1} = π/6, 𝜃_{2} = π/3
= 4.383
Problem 5 :
(3, 7π/4) and (1, π/4)
Solution :
From the given points, we know that
r_{1} = 3, r_{2} = 1, 𝜃_{1} = 7π/4, 𝜃_{2} = π/4
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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