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Chapter 1: Problem 67

\(1^{\circ}=\ldots \ldots \ldots \ldots \ldots\) (a) \(600^{\prime \prime \prime}\) (b) \(3600^{\prime \prime}\) (c) \(180^{\prime \prime}\) (d) \(3600^{\prime}\)

Short Answer

Expert verified
1 degree is equal to: (a) \(1/6^{\circ}\) (b) \(1^\circ\) (c) \(1/20^\circ\) (d) \(60^\circ\)

Step by step solution

01

a) Convert 600'' to degrees

To convert 600 seconds (also referred to as "arcseconds") to degrees, we'll need to first convert seconds into minutes and then minutes into degrees. 1. Divide the total number of seconds by the number of seconds in a minute, i.e., 60: \(600'' / 60 = 10'\) 2. Now, we have 10 arcminutes. Next, we'll divide this by the number of minutes in a degree, i.e., 60: \( 10' / 60 = 1/6^{\circ} \) So, the degree equivalent for 600'' is \(1/6^{\circ}\).
02

b) Convert 3600'' to degrees

To convert 3600 seconds (arcseconds) to degrees, we'll follow the same steps as in part a: 1. Divide the total number of seconds by the number of seconds in a minute, i.e., 60: \(3600'' / 60 = 60'\) 2. Divide the total number of minutes by the number of minutes in a degree, i.e., 60: \( 60' / 60 = 1^\circ \) So, the degree equivalent for 3600'' is \(1^\circ\).
03

c) Convert 180'' to degrees

To convert 180 seconds (arcseconds) to degrees, we'll follow the same steps as in parts a and b: 1. Divide the total number of seconds by the number of seconds in a minute, i.e., 60: \(180'' / 60 = 3'\) 2. Divide the total number of minutes by the number of minutes in a degree, i.e., 60: \( 3' / 60 = 1/20^\circ \) So, the degree equivalent for 180'' is \(1/20^\circ\).
04

d) Convert 3600' to degrees

To convert 3600 minutes (arcminutes) to degrees, we'll divide the total number of minutes by the number of minutes in a degree, i.e., 60: \(3600' / 60 = 60^\circ\) So, the degree equivalent for 3600' is \(60^\circ\).

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