# Unit Circles and Standard Position

## Unit Circles and Standard Position

The general equation for a circle is the quantity of x minus h squared, plus the quantity of y minus k squared equals r squared. Here, h and k are the coordinates for the center of the circle on a coordinate plane, and then r is the radius of the circle. We have something called unit circle, which has a radius of one and the center is at the origin, and the origin is where the x axis meets the y axis.

Which is right there, in the center of the coordinate plane. The coordinates for the origin is 0,0 because it’s that point zero on the x axis and point zero on the y axis. If we were to plug the numbers 0,0 into x -excuse me- into h and k, then we build it we would be able to simplify this equation. Then also the radius is 1, we can plug that in to r right there. We can go ahead and simplify this equation, to get this right here.

Since h and k are zero, we can take those out of the way and then we just plug 1 into r, we square it and we still have 1. This is the equation for a unit circle. We have something called standard position, which is the position of an angle of measure, blank, whose vertex is at the origin. Right here, you see this angle, and I’m just going to label it with the angle symbol, we don’t know what the angle is, but the vertex right here is at the origin of this coordinate plane.

Then, the initial side crosses the unit circle at the point 1,0. This right here is the initial side and meets the circle right there crossing the circle at point 1,0. The initial side is always going to cross the circle at point 1,0. The reason that it’s always going to cross the point 1,0 is because the initial side always has to be on the x axis of the coordinate plane. In order to do that -the y- it must be on the y axis at point zero.

Then the terminal side, which is the other side, the side right here, this is the terminal side. It crosses the unit circle at some other point, we label that point a,b. It meets it right there, and we label that a,b. There’re a few things we conclude from this setup. The sign of angle measure equals b, the co-sign of the angle measure equals a, and then the tangent of the angle measure equals b divided by a. Those are a few things to keep in mind. This is a look at unit circles and standard position.