introduction-to-the-unit-circle

Introduction to the Unit Circle

The unit circle is a circle with a radius of 1

This introductory video covers how to name the points on the unit circle and their degree measure.

Common Core Standard = F.TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

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Transcript

Today we are going to look at the basics of the Unit Circle. When you are working with the unit circle there are three ways to name points on the circle. You can use ordered pairs, degrees, or you can label using radians. Let's first start with the radius of the circle. We are assuming that the radius is 1 unit and we start with center at the point (0,0) Here is our origin of the circle (0,0) This first point is (1.0) the next point will be (0,1) This third point on the left will be (-1.0) and the bottom point on the circle is (0,-1) These are the four ordered pairs of the unit circle. Now let's look at the degrees for each of these points. This point on the right (1.0) can be written either as zero degrees or 360 degrees because a circle has 360 degrees. This point at the top of the circle can be written as 90 degrees because we are 90 degrees away from the x axis. On the left, this is 180 degrees because we have traveled 180 degrees from the first point, and the point on the bottom is 270 degrees because we have added another 90 to 180, and if we go all around the circle it brings us back to 360 degrees. Now let's talk about radians. Here is our point (1.0) now in radians halfway around the circle we call this pi, and all around the circle is 2pi so we have fourths (1/4) so a fourth way around the circle it would be 1/2 pi and 3/4 around the circle would be 3/2 pi so in radians you have 1/2 pi ,pi,3/4 pi , and then 2pi .

This video covers how to label the unit circle.

The unit circle can be labeled using ordered pairs,degree, and radians

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Tagged under: geomeetry,precalculus,circles,unit circle,Trigonometry (Field Of Study),F.TF.1

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