Ways to teach and introduce the unit circle, reference angles, and exact values

I have thought through the best ways to teach students to love trigonometry.  I tell them this is "The Best Unit Ever" because of how great it is for students to first see the relationship between a triangle and a circle.  I am hoping that you will comment on this blog post to give your version of how to begin to introduce trigonometry.
First, I think it is essential to have a few days of "back to basics."  We refresh operations with fractions, simplifying and rationalizing radicals, and basic fraction simplification of of sine, cosine, and tangent ratios.
From this point, I introduce all six trig ratios.  Students primarily work in quadrant one.  They should be able to find all six trig ratios given cosecant of theta = 2/3.
Now for the fun.  I begin by giving two homework questions asking students to find all six simplified trig ratios.  The first triangle is such that sine of theta is 5/10.  I use this so that students will find all six ratios simplified and can refer back to this triangle as they get into making values for any angle with a 30 degree reference angle.  Similarly I use a second triangle such that tangent of theta is 7/7 so that students can refer back to this with any 45 degree reference angle.

Next we begin the whole next class period with the 30 degree triangle that had sides 5, 10, 5root3.  I discuss the unit circle as having a radius of 1.  From there I use the idea of similar triangles to "scale" down the triangle by 10, thus creating a triangle of hypotenuse 1, height of 1/2, and base as root 3 over 2.  We place this into quadrant one.

 

As we started, we only had quadrant one and we took time to label the actual triangle's base and height and discussed how you might write the ordered pair at the edge of the circle.  We also discussed how by looking at the triangle's opposite and hypotenuse we still get sine as 1/2 and why sine is the height or the y value.  They struggle at first with labeling points as with ordered pairs that include square roots.  After this we continued through each of the four quadrants only drawing the triangle and labeling the triangle's sides with 1/2 and root 3 over 2.  As we ended the class period, we were able to use reference angles to label each angle from standard position in degrees (radians were drawn in later).  Students also started to label exact values in ordered pairs.  Their goal in homework was to complete x and y values as ordered pairs.  The next day about half of students had considered positive and negative values since we were in quadrant two or three, etc.  This was great to discuss at the beginning of class.

The next day, we took the 45 degree triangle above and similarly placed it in quadrant one as a whole class activity.  Then students continued working in class on correctly identifying all four quadrants with angles in standard position in degrees  and with ordered pairs. 

Students completed this day's assignment by taking the 30 degree triangle and flipping it to make a 60 degree triangle in quadrant one.  We did this part together and discussed placing x and y values at this mark.  Students were to continue by making the 60 degree bowtie diagram.

I would love to hear comments on how you introduce and teach the first week of trigonometry to your students!