Conversion of angles

Maths and Fun together

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.

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