This is going to be done in two parts: creating the unit circle and tracing the graph.
First thing we're going to need is a square grid. Go to Graph -> Grid Form -> Square Grid. The square grid creates a point at (1,0), select that point and the origin point and construct a circle using Construct -> Centre + Point. Select the circle and construct a point on the circumference. Construct a segment from the origin to that point.
Now we're going to create some lines to track the coordinates of the moving point on the circle. Now create intersections for those lines at the axes. Then hide the lines, we don't need them anymore. Now create line segments from the movable point on the circle to those points. It will make more sense when you look at the next picture. I changed the colours of my line segments, you can too under Display -> Line Color.
That's it for the first part. Now to create the stuff to trace the graph.
Select the point on the y-axis and the y-axis. Construct a perpendicular line.
Select the horizontal line and construct a point on it. Go to Measure -> Coordinates for the point that was just created and the movable point on the circle.
At this point, hide the horizontal line and all of the points I have selected in the following picture.
Next, select the points and go to Measure -> Coordinates. This is going to seem wishy-washy but position the point on the line (the hidden line) on the y-axis and position the movable point on the circle on the x-axis. You'll need to be careful, but it can be done. (It doesn't actually matter if you get to 0.01, the computer is likely truncating some decimal places anyhow.)
Select the point C and go to Display -> Trace. Select the points B and C and go to Edit -> Action Buttons -> Animation...
You may have to test your action button to see if everything is working properly. I had to adjust the settings on mine like in the picture above to ensure that my animation did, in fact, create a sine curve.
Cosine is a bit harder than sine. Click here for cosine!