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# In mathematics, the unit circle is a circle with a radius of one. Frequently, especially in trigonometry, the unit circle is the circle of radius one centered at the origin in the Cartesian coordinate system in the Euclidean plane. The unit circle is often denoted S.

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##### Alisa L.

University of Texas at Austin

##### Martha R.

Michigan State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

circle now, just to kind of review a unit circle is a circle where the origin eyes the center of the circle and that the points on the circle, the radius basically is one unit out here on this graph just so that we could see the circle kind of enlarged. For illustration say each unit on this coordinate graph is actually 1/4. So I've got the circle drone where the coordinates, if you'll notice far out are the exes are either positive one or negative one. And the wives are either one or negative one as far as the intercepts. Okay, so this is what a unit circle looks like. So we're gonna look at sign and cosign and finding those from a unit circle now in a unit circle the terminal side. A point on the terminal side is going to lie on the circle, which means that it's going to kind of be the radius of the circle. So since this point, this is point P. Since P is a coordinates X y or on the unit circle, that means that our is going to equal are one, and we can find sign and cosign from the actual coordinates because our sign of the angle is going to be our y Cordant, and our cosign of the angle is going to be our X coordinate. So we confined our Y and X coordinates easily if we're given the point that lies on the circle and the radius is one because it is a unit circle. So let's look at an example, and we're gonna find the sign and cosign of this. Now we're giving the point where the P is to square root of 2/3 and negative 13 because this is on a unit circle in its in standard position. This means that our our is going to equal one. So we confined our son in our co sign. Now just to kind of review or sign is gonna be our y coordinate. So our sign of this angle is going to equal negative one third and our Kasan of this angle is going to equal are X coordinate, which is to squarer to to over three

Liberty University

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##### Alisa L.

University of Texas at Austin

##### Martha R.

Michigan State University

##### Kristen K.

University of Michigan - Ann Arbor