Trigonometry

Maths and Fun together

This is question 6 of Ex 6.1

Transcript

00:00This is question number 6, exercise 6.1, in this we have to convert the angles into radians.

00:07But in this question we have to use the value of Pi, we don't have to keep Pi in the answer.

00:14That is 3.1416, now what we will do?

00:18Basically, you see what is the relation between degrees and radians.

00:24We have a complete rotation of 360 degrees and that is equal to 2 Pi radians.

00:31We use its simplified form, that is 180 degrees equals to Pi radians.

00:38If you divide 360 by 2 and here also by 2 then you get this relation.

00:45If 180 degrees is equal to Pi radians, then 1 degree will be equal to what?

00:53Very simple, we separate 1 degree.

00:57So 1 degree is basically Pi divided by 1 over 80 radians.

01:04Now we have to use this relation in everything.

01:07Now you see what you will do?

01:09You will multiply 270 degrees by Pi divided by 1 over 80.

01:15But in this question, because they have told us that we have to use the value of Pi.

01:21When you use the value of Pi, it is going to be 3.1416 divided by 180.

01:31When we simplify this, the answer you will get from the calculator is 848.232 divided by 180.

01:45So our final answer is 4.7124 radians.

01:55Try to get up to 4 decimals in angles.

02:00In next question, you have to convert 60 degrees into radians.

02:04We have already deduced that 1 degree is equal to Pi over 180 radians.

02:101 degree is equal to Pi over 180 radians.

02:16You will simply multiply 60 degrees by Pi over 180.

02:23Cancel 0 from 0.

02:25Here you have to use the value of Pi.

02:28That is 3.1416 divided by 18.

02:35When we simplify this question, the answer you will get is 1.0472 radians.

02:52Now come towards third part of this question.

02:57You have 180 degrees and 45 minutes.

03:02First of all, you have to convert minutes into degrees.

03:06You know that 1 degree is equal to 60 minutes.

03:10So when we have to convert minutes into degrees, we have to divide it by 60.

03:16180 degrees plus 45 divided by 60.

03:22So it is going to be 180 plus 0.75, 180.75 degrees.

03:38We are going to convert these degrees into radians.

03:41Very simple.

03:42We know that 1 degree is equal to Pi over 180 radians.

03:48So we are going to multiply this with Pi over 180.

03:55Here you have to use the value of Pi.

03:58Because we don't want to keep Pi in the answer.

04:063.1416 divided by 180.

04:11When you solve this, you will get the answer.

04:16Multiply these two numbers and divide by 180.

04:20You get 3.1547 radians.

04:27Now come towards the last part of this question.

04:3075 degrees, 30 minutes and 45 seconds.

04:341 degree is equal to 60 minutes.

04:37And 1 degree is equal to 3600 seconds.

04:41Because further 60 seconds and 60 into 60 will be 3600.

04:48You will get all these values in degrees.

04:5375 degrees plus 30 divided by 60.

04:59And this is 45 divided by 3600.

05:04This will also be converted into degrees.

05:06And this will also be converted into degrees.

05:09If you divide 30 by 60, it will be 0.5.

05:14It is going to be 75 degrees plus 0.5 degrees plus 0.0125 degrees.

05:32It is going to be 75.5125 degrees.

05:44Now we know that 1 degree is Pi over 180.

05:49Simply multiply 75.5125 by Pi over 180.

05:58Put the value of Pi.

06:0075.5125 into 3.1416 divided by 180.

06:12Multiply these two numbers by a calculator.

06:15Divide by 180.

06:17The final answer you are getting is 1.3179 radians.

06:24If your answer is more than 4 digits.

06:27After decimal point, round off it.

06:30And close it by up to 4 digits.

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