### Polar Coordinates Distance Calculation**Problem Statement:**Two plane polar coordinates have the coordinates \((2.2, 48.3^\circ)\) and \((4.6, 10.5^\circ)\). Calculate the distance between them. Round your answer to 1 decimal place.**Detailed Explanation:**In polar coordinates, a point in the plane is represented as \((r, \theta)\), where:- \(r\) is the radial distance from the origin.- \(\theta\) is the angular coordinate (or angle) in degrees.To find the distance \(d\) between two points \((r_1, \theta_1)\) and \((r_2, \theta_2)\) in polar coordinates, you can use the formula:\[ d = \sqrt{r_1^2 + r_2^2 - 2 r_1 r_2 \cos(\theta_2 - \theta_1)} \]1. For the coordinates \((r_1, \theta_1) = (2.2, 48.3^\circ)\): - \(r_1 = 2.2\) - \(\theta_1 = 48.3^\circ\)2. For the coordinates \((r_2, \theta_2) = (4.6, 10.5^\circ)\): - \(r_2 = 4.6\) - \(\theta_2 = 10.5^\circ\)Convert the angular difference \((\theta_2 - \theta_1)\) to radians if necessary, or use the cosine of the difference directly in degrees:\[ \cos((\theta_2 - \theta_1)^\circ) = \cos(10.5^\circ - 48.3^\circ) \]Then, substitute the values into the formula to compute the distance \(d\).**Note for Educational Websites:**- Ensure that students understand how to convert between degrees and radians if needed.- Explain the cosine function and its significance in the formula.- Provide step-by-step calculations and intermediate results to enhance understanding.Remember to use appropriate mathematical notation and clarify each step for better readability and comprehension.

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Answered: Two plane polar coordinates have the…

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Two plane polar coordinates have the coordinates (2.2,48.3 °) and (4.6,10.50 ), calculate the distance between.

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter6: Uniform Circular Motion And Gravitation

Section: Chapter Questions

Problem 47PE: Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.1011 solar...

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