How does radian measure of an angle compare to the degree measure? Include an explanation of 1 r

step 1 I think this question. Ask us how radiant measures compared to degree measures. Okay, well, if w

How does radian measure of an angle compare to the degree...

Key Concepts

Radian Measure

Radian measure is an angular measurement unit based on the radius of a circle. One radian is defined as the central angle that intercepts an arc equal in length to the radius of the circle. This concept naturally relates the angle to the dimensions of the circle, which simplifies many mathematical and physical formulas.

Degree Measure

Degree measure divides a circle into 360 equal parts, with one degree representing 1/360th of a full rotation. It is a conventional unit that is widely used in various fields. The relationship between degrees and radians is given by the fact that 2? radians is equivalent to 360 degrees, which facilitates conversion between these units.

Transcript

00:01 I think this question.

00:03 Ask us how radiant measures compared to degree measures.

00:06 Okay, well, if we have a initial ray initial side here and we take our angle, we could kick anywhere on the circle and we could say it's some portion of 360 degrees.

00:27 Those arbitrary what i just i took a full circle and i said, ok, let's break up all the different angles we could do starting from this initial side and i'll say, ok, we're working up into 3 64 pieces.

00:47 This one.

00:47 Yeah, there's one here.

00:49 There's one here and one here and i can keep going and there'll be 3 60 different degrees are we could d'oh! half of a degree and 1/4 of a degree.

00:58 It was just a way to break for that angles within this circle and measure them well, there's another natural way to do this than just giving 360 arguably more natural.

01:13 We can use radiant well, what do we know about the conference of this whole circle? if we know the radius, so consider this initial rate as the radius.

01:29 It's art.

01:32 Then we know that that's a conference of an entire circle will be two pi r.

01:39 Okay, so if we actually measure angles by how much of the two pi r we traveled begins.

01:49 Okay, this will be like, when a of the entire circle.

01:59 So because it's 1/8 of two pi r, it's really like one.

02:03 Paul.

02:04 If we went here, we would say it's 1/4 uh, our entire comfort, so ah, hi.

02:17 Oh, times are over.

02:19 Holds two over heart.

02:20 That's just 1/2 for this one.

02:22 Is pi r over and get we could go halfway and this would be all right.

02:33 Say conference, but half of it get something.