0:01
We want to determine how to take angles that are expressed both in degrees and radians one with respect to the other. For example, 75 degrees is given in degrees and I want to express that degree measure, take it to radians. 120 is in degrees, express it to radians. In the third, 5 pi over 6 that is in radians, take it to degrees, as well as 5 pi over 2, that is,
0:33
I want to show you in a simple way, without much complication, how to transform from degrees to radians and vice versa, from radians to degrees. There is a formula for this. The formula says this: alpha, which is the measure of the angle of degrees, over 180, will be equal to the angle of the radian prestations over 180.
1:00
This is the formula that will be used. But I want to omit the formula and teach you how to do it directly, so you don't have to do so much work in the aftertaste of this formula by the rule of three. For example, if we wanted to apply the formula, and I'm going to do it once, I would do the following: How would we transform 75, which is in radians? Simply, I would place 75 where alpha appears, because alpha corresponds to degrees.
1:29
And I would write 75 over 180 equals the radian angle over pi. And simply we are going to clear the radian angle. Clear in radians. We would have the same. Applying the rule of three, I would multiply 75 by pi. I would get 75 pi over 180. And here I start to calculate.
2:03
reduce in the cases that can be 75 has a fifth that would be 15 15 pin 180 has a fifth equal to 36 since 36 times 5 would give me 180 but 36 and 15 both have a third third of 15 would be 5
2:27
and the third of 36 would be 12. This is the most I can simplify. And we have transformed the angle from 75 degrees to radians. 75 degrees, the angle expressed in degrees, equals 5 pi over 12 in radians. But what do we want to do? Not use the formula.
2:52
Let's see how it can be done directly. We use the formula but without the need to get specifically to it. Let's see first, how when I have an angle in degrees, take it to radiate. Simply, let's do the following. Let's take the angle, which is 75 degrees, I'm going to divide it by 180 and I'm going to multiply it by pi.
3:21
Why? Because the equivalence of pi and 180, I repeat, are equivalent. That is, pi represents half the circumference and is equivalent in degrees to 180. That is, if I multiply by pi and divide by 180, I am multiplying and dividing by 1, because they would simplify. Both are 180 to the side and the angle would be 75. That is, the angle with this degree, I divide it by 180 and multiply it by pi and I go in to simplify.
3:49
What did we do here? 75π/180, I'm not going to repeat it, what we did here, and this would be 5π/12. I already have it expressed, what I wanted to do, take it from degrees to radians. Let's do a second one, 120 degrees, I want to express it in radians. I write 120 degrees over 180 multiplied by π. Let's simplify as much as we can, we simplify the two zeros,
4:23
I would have 12π/18. I can continue simplifying because 12 and 18 have sixths. That is, they can be divided by 6. 12/6 would give me 2 and 18/6 would give me 3 and we would obtain 2π/3. The equivalent of 120 degrees to radian. That is, the angle of 120 degrees is equivalent in radians to 2π/3. Let's do the other way around. From radians to degrees.
4:54
If we apply the formula, then this value would be located up here, in radians. And then what I have to clear instead of radians, clear alpha in this formula. Something like that. But I repeat, I'm going to do it directly so that you don't have to use the formula. What are we going to do then? We go from radians to degrees, we are simply going to substitute for its equivalent in degrees, which would be 180 degrees.
5:25
And with this we already solved the problem. 5 by 180 over 6. 6 over 180 would give me 30 degrees. 180 over 0 is 30, times 5. And this would give me, when multiplying, 150 degrees. That is, 5 pi over 6 equals 150 degrees. 5 pi over 12, the same thing. 5 pi over 180.
5:55
divided by 12. I simplify, in this case 12 and 180, when I divide 180 by 12, it would give me 15, and 15 divided by 5 would give me 75 degrees. I already have then expressed my equivalence. Notice that I placed in the fourth the same as it was at the beginning. 75 degrees to radius, and now from radius to radius. One more.
6:26
For you to see it. Any way. An example, the most difficult is radial. An example, 3π, let's say, over 30, for example. How would we do this? It would be 3 by 180, between 30, simple radial is to be valued, simply π is substituted by 180 and I perform the operations indicated.
