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Maths and Fun together
  • 7/15/2024
In this question angles are measured in rafians
Transcript
00:00This is question number 5 from exercise 6.1.
00:03In this question, we have to convert the angles which are provided in degrees into radians.
00:09You have angle measure in degrees and angle measure in radians.
00:15Write the answers in terms of Pi.
00:16What does it mean?
00:17It means that Pi should be in your answer.
00:20First of all, you see what is the relation between degrees and radians.
00:27180 degrees is equal to Pi radians.
00:36180 degrees is equal to Pi radians.
00:42We have to convert degrees into radians, so we will separate 1 degree.
00:49You can write 1 degree is equal to Pi.
00:53You have separated 1 from 180.
00:58You can write 180 into 1 is again 180.
01:03Basically, you have separated 1.
01:05We have to see what is 1 degree equal to.
01:081 degree is equal to Pi divided by 180 radians.
01:14Our question is that we have to convert 45 degrees into radians.
01:19We have to convert 45 degrees into radians.
01:221 degree is equal to Pi divided by 180 radians.
01:25We have to convert 45 degrees into radians.
01:31We have to multiply 45 degrees by Pi divided by 180 radians.
01:37Simplify it.
01:38We need the answer in the form of Pi.
01:41We will not calculate the value of Pi.
01:44What is Pi?
01:45Pi is our famous irrational number.
01:47Its value is 3.1416.
01:51We will leave Pi.
01:53Simplify it.
01:55After simplification,
01:58Simplification means that you divide both the numbers from one table.
02:11It can be simplified further.
02:13Finally, we will get Pi divided by 4 radians.
02:20I have divided both the numbers.
02:23It is necessary that both the numbers come to one table.
02:26So, you will have Pi divided by 4 radians at the end.
02:31In the second question, you have to convert 150 degrees into radians.
02:36Similarly, you will have 180 degrees equal to Pi radians.
02:42So, 1 degree is going to be Pi over 180 radians.
02:49Now, you will simply multiply 150 by Pi over 180.
02:55150 will be multiplied by Pi divided by 180.
03:010 cuts 0.
03:04You get 15 Pi divided by 18.
03:08Now, we will simplify it further.
03:113 x 5 is 15.
03:14Basically, both the numbers will be divided on the table of 3.
03:173 x 5 is 15.
03:183 x 6 is 18.
03:20Finally, you will get the answer in the most simplified form.
03:245 x 5 is 6 Pi.
03:26Our unit has been changed to radians.
03:30In the third part of this question, you have 60 degrees and 30 minutes.
03:36First, you will convert all these into degrees.
03:39Then, you will convert degrees into radians.
03:41You know that 1 degree is equal to 60 minutes.
03:47So, it is very simple.
03:49When we convert these, we will divide 30 by 60.
03:55So that you can convert 30 minutes into degrees.
04:0060 degrees plus 0.5 degrees.
04:04You get 60.5 degrees.
04:08Now, you have to convert these degrees into radians.
04:12We know that 1 degree is equal to Pi over 180 radians.
04:17So, you will simply multiply 60.5 by Pi divided by 180.
04:23We need the answer in the most simplified form.
04:26When we finish the decimal point, we get 1.
04:30When we finish the decimal point, we get 0.
04:42When you multiply 10 by 6, you will get 18.
04:45You will get 2 zeros from here.
04:47Now, we will simplify this.
04:50We will cancel both from the table of 5.
04:53You will get 121 divided by 360 Pi.
04:58This cannot be solved further.
05:00So, this will be our most simplified answer.
05:03So, we have 121 divided by 360 Pi radians.
05:09In the last part, we have 120 degrees.
05:14You have to convert these into radians.
05:17180 degrees is equal to Pi radians.
05:24From here, we deduced that 1 degree is equal to Pi divided by 1 over 80 radians.
05:33When we have to convert, we will multiply 120.
05:38Pi over 180 will cancel 0 and 0.
05:43You will get 12 Pi over 18.
05:47You can simplify this further.
05:51You have to simplify this as much as you can.
05:563 twos are 6 and 3 threes are 9.
06:00So, you will get 2 by 3 Pi radians.
06:04120 degrees is equal to 2 Pi by 3 radians.