Question

How many arcseconds are in a degree?

Answer 1

Hint: This question is related to conversion of one unit to another. In this we need to convert one degree to arcsecond. To convert degree into arcsecond we need to know the relationship between degree and arcsecond. We use the definition of arcminute to establish the relationship between degree and arcsecond.

Complete step by step answer:
Let us try to solve the problem in which we need to find there is, how many arcseconds are in a degree? Before solving we need to know the definition of degree, arcminute and arcsecond. Here are the definition:
Degree: It is a unit of measurement of plane angle. It is usually denoted by the symbol ${}^{\circ }$. A full rotation is equal to $360$ degrees.
1. Arcminute: It is a unit of angular measurement equal to ${\displaystyle \frac{1}{60}}$ of one degree. It is also called a minute of arc.
2. Arcsecond: It is also a unit of angular measurement equal to ${\displaystyle \frac{1}{60}}$ of one arcminute. It is also called the second of arc.

Now, as we know that from the definition of arcminute and degree
$1arcminute={\displaystyle \frac{1}{60}}\mathrm{degree}$....................................$eq(1)$
Also as we know that from the definition of arcsecond and arcminute
$1\mathrm{arcsecond}={\displaystyle \frac{1}{60}}arc\mathrm{minute}$...............................$eq(2)$
 Now putting value of $1$arcminute in $eq(1)$ from $eq(2)$, we get
 $$\begin{gathered} 1\mathrm{degree}=60\times 60\mathrm{arcsecond} \\ 1\mathrm{degree}=3600\mathrm{arcsecond} \end{gathered}$$
Hence in a degree there are $3600$ arcseconds.

Note: In the questions in which we convert between one unit to another unit we just have to apply the definition of the unit. These types of questions of unit conversion are asked in very short answer type questions in exams. Arcminute or arcsecond unit of angular measurement is generally used in astronomy.