What is a Radian Angle? Convert Degrees to Radians & Radians to Degrees

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In this lesson, you will learn what radian angle measure is and how it compares to degree measure. Every circle has 360 degrees, and every circle has 2 Pi radians. The reason is because if we consider a unit circle to have a radius of one, then the circumference of a unit circle is 2 Pi distance units. We can then use the distance around the unit circle to be a new measure of angle, where if we go all the way around the unit circle we travel 2 Pi radian angle units around the circle. This is a much more natural distance unit because it is fundamental to all circles and is not arbitrarily invented or defined. It is a fundamental feature of trigonometry, geometry, and calculus.

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Hellow prof... Its a great lesson for every student learning maths+engineering... Can easily solve conversion of radians to degrees and degree to radian. Can you kindly please upload a vedio on how we get thats numbers. Underroot(2), 1/2 etc...

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The angle subtended by the arc is the linear distance in radians.

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[@rayrainer985]

To better understand the conversion table is for me to see a relationship and that relationship is a ratio of 30° (π r)/180°. The degrees cancel out. 30(π r)/180 = π/6 radians. I think it helps when it makes sense of what the conversion table is doing.

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One thing wasn’t mentioned that I think is helpful that the if one takes the length of the radius and bend it around the circle that rad angle is 1.0 why it’s called radian. Great video.

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Absolutely right, that is how the radian is defined. It is the angle subtended by a length of an arc equal to the radius of that circle. That is how the value of Pi becomes 3.14...

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Simple, a radius is the angle subtended at the center of a unit circle by an arc the length of 1 Thus a radian equals 180/pi degrees

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One way to remember the radians is just devide 180 by every angle u will find the bottom number

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I am the student, but I do not understand why the circumference is 2 pi. I read the description. As I was thinking about it, it became clear. Because the diameter is not one, it is two. O man, this is good.

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I learned that the reason there are 360 degrees in a circle is because ancient civilizations used 360 days in a year for crop harvesting. The earth’s path being a orbital circle around the sun. The earth itself is divided into 360 degrees in longitude and latitude, then 60 minutes to a degree, and 60 seconds to a minute. Which brings us to the clock. 24 hours to a day which is split in two for two twelve hour parts to a day…which is 60 minutes to an hour, 60 seconds to a minute…which 360 is divisible by all.

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I am somewhat new to Trigonometry. However, it seems obvious to me that. Another way to look at and remember the Radians in the first quadrant. Is π/6 is 1/6 of π, a half circle or 180°. π/4 is 1/4 of π, a half circle or 180°. π/3 is 1/3 of π, a half circle or 180°. π/2 is 1/2 of π, a half circle or 180°. It's exactly what it is. It may not be as obvious as you go around the Unit Circle. 3π/2 is Three half circles divided by two. Or one and a half circles, divided by two. 3/2 or 1 1/2 divided by 2. Which is of course is 3/4 of the circle and 270°. 5π/4 is 1and 1/4π or half circles 225°. 2π/3 360°÷3 120° Or 2×180°÷3=120°. 3π/3 does reduce as you said. To 1π or π which is 180°. Although 3×180°= 440° and 440°÷ 440°=1, in this case π. As you said one half circle, or 180°. 4π/3 reduces to 1 1/3 π 240°. 5π/3 reduces to 1 2/3π 300°. 180°+ 2/3 180° which is 120 totals 300°. 300° is also Five sixths of the circle. 6/6 of a circle is obviously a whole circle 360°. Even though 6π totals 1080°. 1080°÷1080°=1in this case a full circle. Which makes sense why some prefer to use degrees. 6/6 of a circle intuitively should total 360°. I think the 1080° along with the increments leading up to it will make more sense. As I learn more about Trigonometry and it's related subjects. Although I may have lost some people describing this. I hope this helps. It wasn't my intention wasn't to negatively critique you or the contents of this video. I enjoyed it. As well as all of your other videos I have seen. I think you did a great job of explaining everything. I have only seen a small number of your videos. However, I have found them to be very informative. Thank you for this video. As well as all of your other ones.

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As soon as the sequence is all done I will definitely upload to the app. Thank you!

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