Calculation of degrees minutes and seconds. Converting degree measures to protractor divisions
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Instructions
It's very simple: 1 degree is divided by 60, which are “minutes”. And each minute in turn contains 60 “seconds”. As you can see, there is a complete analogy with those minutes and seconds, which for us have always been more connected with the measurement of time than with angles and coordinates. We owe such a convenient uniformity of dimension to the inhabitants of Babylon, from whom all these minutes, minutes and seconds were inherited by modern civilization. The Babylonians used the sexagesimal system.
Of course, in addition to minutes, there are also smaller fractions. Unfortunately, this is where ancient simplicity ends and modern simplicity begins. It would be logical to divide seconds into 60 shares, or at least into the usual milliseconds, microseconds, etc. But both in the SI system and in native GOSTs it is not recommended to do this, therefore fractions of a degree smaller than an arcsecond should be recalculated in radians. Fortunately, measuring such small angles may only be necessary for sufficiently trained people. But you and I may encounter simpler problems.
So, in order to convert the angle value indicated in the format (degrees minutes seconds) into decimal fractions of a degree, you should add the number of minutes divided by 60 and the number of seconds divided by 3600 to the number of whole degrees. For example, the geographical coordinates of one wonderful place in Krasnodar - 45° 2" 32" northern and 38° 58" 50" eastern. If we convert this to ordinary degrees, we get 45° + 2/60 + 32/3600 = 45.0421° north latitude and 38 + 58/60 + 50/3600 = 38.9806 east longitude.
This is easy to do in a calculator, but you can also use online resources. On the Internet you will be offered to convert seconds, radians, revolutions, and even into miles with a slight movement of the mouse, if the desire arises! Here are some links to online angular coordinate converters:
http://convertr.ru/angle/
http://www.unitconversion.org/unit_converter/angle.html
http://www.1728.com/angles.htm
http://www.fcc.gov/mb/audio/bickel/DDDMMSS-decimal.html
http://www.cleavebooks.co.uk/scol/ccangle.htm
http://convert-to.com/120/angle-units.html
http://www.engineeringtoolbox.com/angle-converter-d_1095.html
Sources:
- how to convert degrees
A watch is one of the most necessary things in modern world. Even small children can use the minute and hour hands to accurately indicate the time to sleep, eat or watch their favorite show. The basic units of time are hours, minutes and seconds. To define large time periods, concepts such as days, weeks, months and years are used. However, let’s focus on minutes and seconds and try to look at the ways in which one value can be converted into another.
You will need
- - calculator or internet access
Instructions
If you are not given an integer, for example, 4 minutes 16 seconds, then you need to multiply the number of minutes by sixty, and then add the remaining seconds to this. Mathematically it will look like this: 4*60+16=256. Total, 256 seconds.
Please note
In addition to counting time intervals, minutes and seconds are used in astronomy and geometry. Sometimes they replace degrees.
The word "second" comes from the Latin secunda divisio, which can be translated as "second division", that is, an hour divided twice by 60.
The designation "minute" also comes from Latin. It is believed that this word was derived from minutus - “small”. In ancient times there was a definition of a minute. Based on today's value, one such minute was equal to 24 present minutes. A similar designation is periodically found in ancient works of astronomers.
How to convert time from one unit of measurement to another. For example, convert seconds to minutes and hours and vice versa.
You will need
- Calculator
Instructions
To convert seconds to hours, just divide the number of seconds by 3600 (since there are 60 minutes in one hour, and 60 seconds in each minute). To do this, you can use an ordinary calculator. Even the one found in almost any cell phone will suffice.
However, it should be taken into account that the number of hours will probably be fractional (in the form of a decimal fraction: x.y hours). Although the decimal format of representation (of time intervals) is more convenient when carrying out intermediate calculations, the representation is used relatively rarely as a final answer.
Depending on the specific task, you may need to specify the time in: x hours y seconds. In this case, it is enough to divide the number of seconds by 3600 - the whole part of the division will be the number of hours (x), and the remainder of the division will be the number of seconds (y).
If the end result is a specific moment in time (clock reading), then the solution will probably need to be presented in the form: x hours, y minutes, z seconds. To do this, the number of seconds will first have to be completely divided by 3600. The resulting quotient will be the number of hours (x). The remainder of the division must again be completely divided by 60. The quotient obtained at this step will be the number of minutes (y), and the remainder of the division will be the number of seconds (z).
In order to solve the problem, i.e. convert seconds to hours, all the above steps must be done in reverse order. Accordingly, for the first case, the number of seconds will be x.y*3600, for - x*3600+y, and for the third - x*3600+y*60+z.
Although using the above method should not cause difficulties for single calculations, for large volumes of calculations (for example, processing experimental data), this process can take a lot of time and also lead to errors. In this case, use the appropriate programs.
For example, using MS Excel, you only need to enter the required formulas once to get ready-made results. Drawing up suitable formulas does not require programming skills from the user, or even from a school student. For example, let's create formulas for our case.
Let the initial number of seconds be entered in cell A1.
Then in the variant the number of hours will be: =A1/3600
In the second option, the number of hours and seconds will be: =INTEGER(A1/3600) and =RESIDENT(A1;3600) respectively.
In the third option, the number of hours, minutes and seconds can be calculated using the following formulas:
INTEGER(A1/3600)
INTEGER(REM(A1,3600)/60)
REST(REMAT(A1,3600),60)
The radian, the basic unit of measurement for plane angles in modern mathematics and physics, is defined as the angular value of an arc whose length is equal to its radius. Thus, the total angle is 2π radians.
Video on the topic
Please note
Remember that the angle value in degrees varies from 0 to 360.
Useful advice
You can quickly convert angle values from radians to degrees if they are multiples of Pi. For example, if the angle is equal to Pi, then its value in degrees is equal to 180. If the angle is equal to Pi/2, then its value in degrees is equal to 90.
Sources:
- how to convert degrees radians to 2019
The duration of some processes is presented in ah. But if the numbers 15 minutes or 40 minutes are easy to qualitatively evaluate as a period of time, but may need to be converted into watch And large number minutes to make it easier to understand or for further calculations.
Instructions
Video on the topic
Measuring quantities in ah, minutes and seconds is most often used to indicate geographical or astronomical coordinates. As in measuring time, each minute of arc contains 60 seconds, and each degree contains 60 minutes. This sexagesimal number system has been preserved since the times of ancient Babylon. But in modern systems standardization, including the SI used in Russia, uses decimal calculation, so quite often it is necessary to convert minutes and seconds into decimal fractions of a degree.
Instructions
Divide the number of seconds you know by 3600 to convert them to degrees. Since one arc contains sixty arc seconds, and one contains sixty arc minutes, the seconds in a degree should be 60 * 60 = 3600.
Use for practical calculations, since calculations accurate to thousandths require very rare mathematical abilities. For example it could be standard calculator Windows OS. To launch it, you need to click the “Start” button (or press the WIN key), go to the menu in the “Programs” section, then to its “Standard” subsection and select “Calculator”. You can do this another way - press the WIN + R key combination, type the calc command and press the Enter key.
Enter the known number of seconds by clicking the buttons in the on-screen calculator interface or using the keyboard. Then click the slash key and enter the number 3600. Then press the equal sign and the calculator will calculate and show you the value in , corresponding to the specified number of seconds.
Use calculators if you don’t have any others at hand. For example, you can enter a query with the desired mathematical operation into the search engine Google system, and she will show you the result by calculating it on her own calculator. Let's say, if you need to find out the value of 17 seconds in degrees, then enter the following query into Google: “17 / 3600”. It is not necessary to press the search button.
Usually, along with seconds, you also need to count minutes, since geographic coordinates are indicated in the format “degrees minutes seconds” (° " "). For example, the coordinates of the most visited place in the city of Krasnodar are 45° 01" 31" and 38° 59" 58" East. To convert the longitude of this place to a fraction of a degree, you need to add minutes expressed in degrees (59 / 60 = 0.983) and seconds expressed in degrees (58 / 3600 = 0.016) to 38 whole degrees. If you recalculate latitude using the same algorithm, the coordinates in degrees will look like this: 45.025° north latitude and 38.999° east longitude.
Sources:
- degrees to seconds
If you measure a segment (arc) on a circle, the length of which is equal to the radius of this circle, you will get a segment whose angle is considered to be equal to one radian. The measurement of plane angles in these units is usually used in mathematics and physics, and in applied sciences: geography, astronomy, etc., angular degrees are more often used for the same purposes, minutes and seconds.
Instructions
Use Pi to determine the proportion between angles and radians. This constant determines the constant ratio of the circumference of a circle to its radius. Since radian is also expressed as the circumference of a circle, it is possible to establish a correspondence between them. The circumference of a circle is two times the radius times Pi, and the length of an arc that makes an angle of one radian is equal to one radius. Dividing the first by the second, we get a value equal to two Pi numbers - that’s how many radians fit in a full rotation (360°). This means that one radian corresponds to 180° divided by Pi - this is approximately 57.295779513° or 17 arc seconds and 44.806 arc seconds, which corresponds to 3437.75 arc minutes.
Divide the known angle in arcs by 3437.75 to find the angle in radians. For example, if the angle is 57 minutes, then the same angle, measured in radians, will be equal to 57/3437.75 = 0.0165806123.
Use a calculator of some kind for practical calculations. This can be a separate gadget, software from the operating system, a computer built into search engine or a script calculator hosted on a website. For example, for calculations using the calculator built into Google search engine, just go to it home page http://google.com and enter the desired mathematical operation in the field search query. The same calculator is built into the search engine http://nigma.ru. If you decide to use the built-in operating system Windows calculator, then you can find a link to launch it in the main menu on the “Start” button. Having opened it, you need to go to the “All Programs” section, then to the “Standard” subsection, then to the “Service” section, and then select the “Calculator” item.
Video on the topic
Sources:
- Online converter of arc minutes to radians
Coordinates objects can be written in several forms: in degrees, minutes and seconds (ancient method), in degrees and minutes with a decimal fraction, and also in degrees with a decimal fraction (modern version). Today all three methods are used, creating the need for translation geographical coordinates from one system to another.
You will need
- - coordinates in one of the recording forms;
- - calculator;
- - translation program and computer.
Instructions
If you are given coordinates in decimals, convert them and minutes. First calculate the latitude. To do this, rewrite the number before the decimal point or period, this will be the number of degrees. Then convert the fractional part to: multiply it by 60. The resulting number will be your latitude. Do the same operation with the longitude of the point. Write down the resulting coordinates as 12°45.32N, 31°51.06"E.
With the development of mathematics, and science in general, it turned out that in many cases it is more convenient to express the magnitude of an angle in fractions of the circle “subtracted” by the angle - radians. And they, in turn, are “linked” to the number pi = 3.1415926..., which expresses the ratio of the circumference of a circle to its diameter.
Pi is an irrational number, that is, an infinite decimal fraction. It is impossible to express it as a ratio of integers; today billions and trillions of decimal places have already been counted without any signs of repeating the sequence. What then is the convenience?
In expression trigonometric functions(sine, for example) of small angles. If you take a small angle in radians, then its value will be equal to its sine with a high degree of accuracy. In scientific and, especially, technical calculations, it has become possible to replace complex trigonometric equations simple actions arithmetic.
Plane angles in radians
In science and technology, it is also most often more convenient to use its radius instead of the diameter of a circle, so scientists have agreed to assume that a complete circle of 360 degrees is an angle of two pi radians (6.2831852... radians). Thus, one radian contains approximately 57.3 angular, or 57 degrees 18 minutes of arc of a circle.
For simple calculations, it is useful to remember that 5 degrees is 1/36 of pi, and 10 degrees is 1/18 of pi. Then the values of the most common angles, expressed in radians through pi, are easily calculated in the mind: we substitute the value of the fives or tens of the angle in degrees into the numerator 1/36 or 1/18, respectively, and multiply the resulting fraction by pi.
For example, we need to know will be at 15 angular degrees. There are three fives in the number 15, which means the fraction is 3/36 = 1/12. That is, an angle of 15 degrees will be equal to 1/12 radian.
The obtained values for the most commonly used angles can be summarized in a table. But it is more clear and convenient to use a circular angular diagram like the one shown on the left side of the figure.
Spherical angles
The corners are not only flat. A spherical (or spherical) sector of a sphere of radius R is uniquely described by the angle at its vertex phi. Such angles are called solid angles and are expressed in steradians. A solid angle of 1 steradian is the angle at the vertex of a circular spherical sector with a base diameter (bottom) equal to the diameter of the circle R, as shown in the figure on the right.
However, it should be remembered that there are no “stegraduses” in the scientific and technical lexicon. If you need to express a solid angle in degrees, then they write like this: “a solid angle of so many degrees,” “the object was observed at a solid angle of so many degrees.” Sometimes, but rarely, instead of the expression “solid angle” they write “spherical” or “spherical angle”.
In any case, if the text or speech mentions solid, spherical, spherical angles and, in addition to them, plane ones, they must be clearly separated from each other in order to avoid confusion. Therefore, in such cases, it is customary not to simply use “angle”, but to specify it: if we are talking about a flat angle, it is called the arc angle. If it is necessary to provide technical ones, they also need to be specified.
For example: “The angular distance on the celestial sphere between stars A and B is 47 minutes of arc”; “An object observed at a heading angle of 123 degrees was visible at a solid angle of approximately 2 degrees.”
Video on the topic
Most artillery problems involve calculating angles and ranges. In this case, angles in artillery are usually expressed in divisions of a protractor. However, engineering microcalculators produced by our industry and imported perform mathematical operations with angles expressed in degrees (DEG), degrees (GRAD) and radians (RAD). Grads and radians are practically not used in artillery calculations. Therefore, when solving many artillery problems, it is necessary to convert the angles specified in the divisions of the protractor into degrees and vice versa.
The conversion of degree measures into inclinometer divisions is carried out according to the table for converting degrees and minutes into inclinometer divisions (Appendix 1). The conversion of goniometer divisions into degree measures is carried out according to the table (Appendix 2).
Example 1. Convert the directional angle from the degree measure = 21337 into protractor divisions:
Solution: From the table 180= 30-00.0
––––––––––––––
21337= 35-60.3
Example 2. Convert the directional angle from the divisions of the protractor into a degree measure = 35-60.3
Solution: From the table 35-00 = 210
0-60 = 336
0-00.3 3.6 1
––––––––––––––
35-60.3 = 21337
Converting a degree measure to protractor divisions and vice versa can also be done using a microcalculator. To translate the angle , given in the divisions of the protractor, the coefficient is applied to the degree measure using a microcalculator TO G= 6. The value of this coefficient is determined based on the ratio known in artillery:
To obtain an angle in degrees, the angle entered into the microcalculator in the divisions of the protractor, while separating the large divisions from the small divisions of the comma, must be multiplied by the number 6, i.e.
= 6 (3)
Example 3. Target directional angle c = 6-73. Determine the value of this angle in degrees.
Solution. 
.
The inverse problem - converting an angle from a degree measure to inclinometer divisions - is solved using the same coefficient TO G= 6 according to the formula:
= 6. (4)
Example 4.
When determining topographic data on a target using a microcalculator, the topographic directional angle of the target in degrees was obtained 
determine the value of this angle in divisions of the protractor.
Solution. 
17,89
= 17-89.
Transition from arc minutes and seconds to decimal degrees and vice versa.
If the angle is given in degrees, minutes and seconds, then before moving on to the protractor divisions, you must first convert it to degrees and decimals of a degree. The transition from arc minutes and seconds to decimal degrees is made using the formula:
,
(5)
Where – angle in degrees and decimals of a degree;
WITH– number of seconds;
M– number of minutes;
G– number of degrees.
Example 5. Using formula (5), recalculate the angle = 171524, expressed in degrees minutes and seconds in decimals of a degree.
Solution. 
Many inexpensive imported microcalculators have a button for converting angles specified in degrees, minutes and seconds into degrees and decimals of a degree.
or – button to convert to degrees and decimals of degrees.
This button makes translation much easier.
To translate, you need to enter the angle value on the calculator in the form: degrees, comma minutes and seconds without division (17.1524), and then press the translate button. The calculator will display the angle in degrees and decimals of a degree (17.25666...).
Transition from degrees and decimals of degrees to degrees minutes and seconds is performed in the following sequence:
Convert decimals of degrees to minutes and decimals of minutes using the formula:
M = (– G)60; (6)
Convert decimals of minutes to seconds using the formula:
WITH= ( M – M)60; (7)
Where M – number of minutes and tenths of a minute;
WITH– number of seconds;
Example 6. Recalculate the directional angle = 17.25666 given in degrees and decimals of a degree into degrees, minutes and seconds:
Solution:M = (17.25666– 17) 60 = 15.3999…;
WITH = (15.39999 – 15) 60 = 23.9999…= 24;
Therefore, the angle in degrees, minutes and seconds will be: 171524.
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