When we think about the degrees of our Unit Circle, we start with the knowledge that any circle is comprised of 360 degrees.
We then imagine forming angles within our circle with the vertex always at the center, (0,0) and with one side, or ray, of our angle always being the x-axis.
The process is described in words below, but you might also find the short video helpful to watch.
We then imagine forming angles within our circle with the vertex always at the center, (0,0) and with one side, or ray, of our angle always being the x-axis.
The process is described in words below, but you might also find the short video helpful to watch.
- If we imagine a second ray also drawn from the origin to the point (1,0) along the x-axis, we consider that Zero degrees.
- We can easily imagine that an angle now drawn with a second ray along the y-axis towards (0,1) shows us a right angle of 90 degrees, a third angle extending in the opposite direction along the x-axis towards (-1,0) would produce a straight angle of 180 degrees, and a fourth angle with a ray extending down along the y-axis towards (0,-1) would produce a reflex angle of size 270 degrees (180+90).
- If we finish the circle back with both sides of our angle lying along the x-axis we now have an angle of the full 360 degrees.
The divisions of the rest of the degrees marked off on the Unit Circle are based on multiples of 30 and 45 degrees. (You can also choose to think of some of the divisions as multiples of 60 degrees - although 60 is of course also a multiple of 30.)
The reason for the choices of 30, 45, and 60 degrees is that our Special Right Triangles (SRTs) play a starring role in Trigonometry. Using the hypotenuse with a unit of 1 (for our Unit Circle's radius of 1) and employing the Pythagorean Theorem, we have the following calculations:
(We will discuss the importance of the calculations later on in our section on coordinates.)
Therefore if we count off angles around our circle with multiples of 45 degrees only we have the following markings:
Using multiples of 30 (and 60) degrees, our circle gains additional angles and looks like this:
Please continue our journey with the radians page.