in the previous video we looked at how angles are measured using degrees this angle would measure around 30° a right angle would measure 90° a straight line 180° and one complete rotation 360° do you know why 360° it's somewhat arbitary and had something to do with the base 60 number system do we have some other way in which we can measure angles such that it makes a little more sense yes that brings us to the concept of radians and trust me not many people understand what radians mean most people know how to convert from degrees to radians and vice versa but it ends there to understand what radians mean let's draw a circle let Point O be its Center and length R be its radius now let me take this length R and place it here at this point now all I do is push it onto the circumference of the circle the length of this red part is still R it has just become curved and that's all the curved length R starts from here and ends here now from the center of the circle we draw another radius that joins the other end point of the red curve this length will also be r as it's the radius let's analyze the figure we have an arc of length equal to the radius of the circle and two radi joining the center and and the end points of that Ark remember the length of the Ark is equal to the radius of the circle this angle formed here is one radian that's the concept of radians actually there's radius everywhere around this angle r r and r and that's probably why they call it radians according to various scientists and mathematicians this is a more logical way to measure angles it's because we're measuring the angle in relation to the radius of the circle but how are radians related to degrees what would this angle be equal to in degrees if you understood the concept of radians well then understanding the conversion between degrees and radians would be a walk in the park what is the circumference of a circle it's 2 pi r where R is the radius of the circle we are talking about the circumference which is the entire boundary of the circle now listen to the next question well how many such are s would you need to cover the entire boundary of the circle let me repeat the question how many such arcs of length R would you need to cover the circumference of the circle pause the video and see if you can work through this on your own the length of the Ark is r and the circumference is 2 pi r yes 2 pi r it means we would need 2 pi such arcs to cover the circumference 2 pi arcs what does that mean as Pi is approximately 3.14 we would need 6.28 arcs to cover the circumference how would it look this is one Arc 2 3 4 5 6 and a little part left for 0.28 ark or 28% of an ark so we need 2 pi arcs to cover the entire circumference and what does each AR correspond to at the center we have seen that one Arc corresponds to one radian at the center it implies that to complete one full rotation we would need 2 pi radians and it tells us something more too if we rotate one arm completely then 2 pi radians will be covered at the center but wait hold on we also know that one full rotation equals 360° yes one full rotation equals 360° as both equal one full rotation these two will be equal 2 pi radians will equal 360° that's the relation between degrees and radians this is what we have been working towards in this video if we understand this we can easily derive the rest this is one full rotation then how many radians will 180° be equal to if we divide this equation by two we get Pi radians equal to 180 ° and 180° is half circle or a straight line and what about a right angle if we divide this equation by two we get Pi / 2 radians equal to 90° so a right angle is equivalent to PI by 2 radians these three relations are most important when it comes to conversion between degrees and radians and we don't really need to remember all three knowing just one is enough and we can derive the rest and now we come to the last and the most important point of this video what does one radian equal to in degrees if we divide the first equation by 2 pi we get one radian as 360 over 2 pi de substituting the value of pi as 3.14 we get the approximate value of one radian as 57.2 n58 de that's the degree measure of one radian if we have an angle like this which measures 1 radian it will equal 57.2 n58 de