Hi class welcome back to our channel for this video I will show you how to convert degree measure to region measure and vice versa okay so number one to convert a degree measure to region multiply it by pi over 180 degrees. Okay, so if our degree measure is given, so since we have a degree guys, in our denominator, it means it can cancel, then we can convert now our given into region measure. Okay, next number two, to convert a region measure to degree, multiply it by 180 degrees over pi.
Normally, when the region measure is given, we can see a pi there. If we multiply the given by 180 over pi, since the pi is in the denominator, it will cancel and the given will now convert into degrees. Okay, so in our diagram, you can see here some special angles given their degree measure and their corresponding radian measure.
So as you can see, 180 degrees is the same as pi. Okay, so now if we divide this by 6, 180 divided by 6 is equal to 30 degrees. and that is also equals to pi over 6. Tama?
So, kung i-divide naman natin ito guys by 3, so 180 degrees divided by 3, that is 60 degrees, and that is also equals or equivalent to pi over 3. Okay? So, ngayon guys, try naman natin mag-convert ng ibang measurement from degree to region and vice versa. Okay, so let's have example number one.
Convert each degree measure into radians. So, if you remember earlier, when we convert degrees to radians, we will just multiply our given by pi over 180 degrees. Okay? So, this time, our degrees will be cancelled.
So, we have 325 pi. over 180. Right? So now, we will just lower the term to 325 and 180. So commonly, we will divide that guys, 5. Since they are both divisible by 5. Right? So 325 divided by 5, that is 65 pi.
Over 180 divided by 5, we have 36. Okay, so this is their region measure. Okay? Next, number two, we have 60 degrees. So, we already did that earlier.
So, now, let's try to multiply that by pi over 180. So, our degrees will be cancelled. So, we can cancel guys 60. This will be 30 or 3. Then, 60 will be 1. Right? So, 1 times pi, that is pi over 3. Okay? Next, number 3, we have negative 315 degrees.
So, same procedure. Multiply natin to guys by pi over 180 degrees. So, maka cancel yung degree.
Then, we have negative 315 times pi that's negative 315 pi over 180. Tama? So, ngayon, try natin iloves term. So, since the numerator and denominator are both divisible by 45, so, try natin yan i-divide dito. Negative 315 divided by 45, that is negative 7. So we have negative 7 pi over 180 divided by 45 that is equals to positive 4. Okay, so therefore yung negative 315 degrees natin is the same lang with negative 7 pi over 4. Okay, last number 4 we have 575. degrees so again multiply lang natin guys by pi over 180 so maka cancel yung degrees so yung 570 and 180 pwede natin yan guys i divide by 30 tama so by cancellation method 570 divided by 30 that is equals to 19 then yung 180 divided by 30 that is 6 Okay, so multiply natin 19 times pi that is 19 pi over positive 6. Okay, naintindihan ba guys kung paano mag-convert ng degree to regions? So let's proceed now to converting region measure into degrees.
Okay, number 1, we have 65 pi over 36. So now, we will convert this into degrees. If you remember the procedure earlier, we will multiply the region measure by 180 degrees over pi. So this will cancel.
After you cancel pi, let's try to simplify or lower the terms. So, first, our 180 here, it can be cancelled by 36. Right? 36 will become 1 and our 180 will become 5. Right? So, we divided it by 36. So, now, let's multiply this.
65 times 5, that is equal to 325 degrees. Okay, then yung denominator natin parehas ng 1 times 1, so 1, so okay na yun. Next, number 2, we have pi over 3, so again, multiply natin by 180 degrees over pi, so maka-cancel yung ating pi.
Then yung 180 degrees, divide natin by 3, so maka-cancel yan, we have 1, then 60. Tama? So 1 times 60, we have 60 degrees. Then our denominator, we have 1 times 1, so 1. Okay? So 60 degrees is our final answer.
Next, number 3, we have negative 4 pi over 3. So applying the same procedure, multiply it by 180 degrees over pi. So our pi will be cancelled. Then, we divide 180 by 3, so that is 60 degrees. Right?
Next, let's multiply. We have negative 4 times 60, that is equal to negative 240 degrees. Okay? So, last one, number 4. So, let's multiply by 180 degrees over pi. So, the pi will get cancelled.
Then, we divide 180 by 4. This will get cancelled. So, this is 45. Correct? So, negative 7 times 45 degrees, that is negative 315 degrees.
Okay, so these are our final answers. Did you understand, guys? So this is the end of our video.
I hope you understand how to convert region measure into degrees measure and vice versa. So if you have questions or clarifications, kindly put them in the comment section below. Thank you guys for watching.
This is Prof. D. I'll catch you on the flip side. Bye!