Any bodies whose shape is round, such as a sphere or circle, require special units of measurement that are different from those for linear objects. These units were degrees and radians. This often raises the question of how to convert degrees into minutes, seconds, and into a radial measurement system.
Units: degrees
About a thousand years BC, the ancient Babylonians used a system for measuring celestial bodies, according to which the entire celestial sphere was divided into 360 equal parts, which was recorded as 360 °. They called one three hundred and sixtieth part a degree.
Since the system of calculus of the ancient Babylonians was six-decimal, they divided each degree into 60 equal parts, and one such part was called the minute and was designated 1 '. In turn, each minute was divided into another 60 parts, 1/60 of a minute was called a second and designated 1 ''.
Our system of calculus, in contrast to the system of the ancient Babylonians, is decimal, however, in the field of measuring round and spherical shapes, degrees, minutes and seconds are still used in their original understanding. For example, a right angle is an angle of 90 °, one degree contains 60 minutes, and one minute is 60 seconds. This information is recommended to remember, because it helps to understand how to translate degrees into minutes.
Unit Type: Radians
Along with degrees, other units of measurement are often used - radians (from lat. Radii - radius). Radian is a more suitable unit of measurement for round bodies, since it is directly related to their geometry. So, one radian is an angle that relies on the length of the arc of a circle equal to its radius. Since the circumference is calculated by the formula L = 2piR, where pi is the number pi equal to 3.14, the full circle is 2pi radians.
The measurement of angles in radians is very convenient in trigonometry, where the calculations and transformations of trigonometric functions are performed in this calculus. For example, sin (pi / 2) = 1.
How to convert degrees to minutes, seconds and radians
How to do it right? To perform the conversion of degrees into minutes and seconds, you need to remember that in minutes it is 60, and in seconds 60 x 60 = 3600 or 1 ° = 60 'and 1' = 60 ''.
We give an example: there is an angle a = 12 °. How to convert degrees to minutes for him? To do this, we compose the proportion from which we get: a = 60 'x 12º / 1º = 720'. Now consider a more complex case: there is an angle a = 32º 45 '23' '. To translate this angle into minutes, you must resort to the addition in minutes of each of its categories. As a result, we get: a = 32 x 60 + 45 + 23/60 = 1965.383 '. In seconds, this angle will be: a = 32 x 60 x 60 + 45 x 60 + 23 = 117923 ''.
To translate the angle a from the example above into radians, you need to remember that 360 ° = 2pi. Now you need to bring the specified angle to degrees, we get: a = 32 + 45/60 + 23/3600 = 32.75639 °. The angle obtained in degrees through the proportion is converted into radians: a = 2pi x 32.75639 ° / 360 ° = 0.5717 radians.