Skip to playerSkip to main contentSkip to footer
Maths and Fun together
  • 7/16/2024
In this question angles are converted into degrees, minutes,and seconds
Transcript
00:00This is question number 7, exercise 6.1. Try to follow radian measure of angles in degrees, minutes and seconds.
00:07Basically, when we convert radian into degrees, minutes and seconds,
00:12this is our hexadecimal system.
00:15You have pi by 4 radians in the question, which you have to convert into degrees.
00:20And after that, if there is any decimal part in the question,
00:24then we will convert it into minutes and seconds.
00:28First of all, you should be clear about the relation between degrees and radians.
00:34180 degrees is equal to pi radians.
00:39Now, if we want to convert radians into degrees,
00:46then you will separate one radian.
00:48So, when we separate one radian,
00:50then you will get 180 divided by pi.
00:57You will multiply pi by 4 by 180 divided by pi.
01:04Pi will cancel.
01:07180 divided by 4 will give you a simple answer.
01:10That is 45 degrees.
01:14That means you have pi by 4 radians.
01:18They are just equal to 45 degrees.
01:24In second part of this question, you have 5 pi by 6 radians.
01:29Now, when we separate one radian,
01:33that means one radian is equal to 180 divided by pi degrees.
01:39You will multiply 5 pi by 6 by 180 divided by pi.
01:46Pi will cancel out.
01:49You will solve it further.
01:51Multiply 5 by 180.
01:54You will get 900 divided by 6.
01:59It will be equal to 150 degrees.
02:03That means 5 pi by 6 radians is equal to 150 degrees.
02:12Radians and degrees.
02:14Both of them are units to measure angles.
02:17In third part, you have pi by 12 radians.
02:22Now, you know that one radian is equal to 180 divided by pi degrees.
02:31Simply multiply pi by 12.
02:35180 divided by pi will cancel out pi by pi.
02:40When you divide 180 by 12, you will get 15 degrees.
02:46In fourth part, you have 7 pi by 40 radians.
02:50We will solve it similarly.
02:52One radian is equal to 180 divided by pi degrees.
02:57Simply multiply 7 pi by 40 by 180 divided by pi.
03:04Pi will cancel out pi by pi.
03:06When you solve it, cancel 0 by 0.
03:12Multiply 7 by 18.
03:14You will get 126.
03:18When you divide 4 by 4, you will get 126.
03:24126 divided by 4 will be equal to 31.5 degrees.
03:29Now, we don't need this point.
03:31We will change it in minutes.
03:36Now,
03:4431.5
03:50Divide 31 degrees and multiply 0.5 by 60.
03:5560 minutes in one degree.
03:5831 degrees will be equal to 30 minutes.
04:05In fifth part, you have one radian.
04:10One radian is equal to 180 divided by pi.
04:24We will convert it in minutes and seconds.
04:28So, we will put pi value here.
04:30What is pi value?
04:32You have only one question.
04:36One radian is equal to 180 divided by 3.1416 which is equal to 57.2956.
04:54You have to take up to 4 decimals in the question of angles.
04:59Now, we will separate the decimal portion.
05:0357 degrees.
05:05Now, you have to convert 5 radians in degrees.
05:10We all know that one radian is equal to 180 divided by pi degrees.
05:14Simply multiply 5 by 180.
05:18Now, put decimal value instead of pi.
05:223.1416
05:24You can remember it or use calculator to calculate it.
05:29When we solve it,
05:34First of all, I have divided both of them.
05:37I am having 57.2956.
05:41You have to take up to 4 decimals.
05:43You will get it.
05:45After multiplying these two now,
05:47286.478
05:50You can solve it with the help of calculator.
05:54Now, you have these two degrees.
05:56Now, we have to take it further in minutes and seconds.
06:00Very simple.
06:02Your integral part or your degrees.
06:05Your decimal part.
06:07Multiply 60 in it.
06:09So, it is going to be converted into minutes.
06:12286 degrees.
06:15Now, you will get 28.
06:200.68
06:22Now, you can see that
06:24Integral part will become minutes.
06:28Now, we will multiply decimal part by 60.
06:31So, it will be converted into seconds.
06:33286 degrees.
06:3528 minutes.
06:370.68
06:39Multiply it by 60 again.
06:41It will be converted into seconds.
06:44So, final answer is
06:47286 degrees.
06:4928 minutes.
06:5140 seconds.
06:53It means that
06:55The 5 variances you have
06:57They are equal to
06:59286 degrees.
07:0128 minutes.
07:0340 seconds.