Topics:
• Trigonometry topic: special right triangles (continued)
The two important right triangles are:
• The isosceles right triangle,
• The half of an equilateral triangle – which I will call the half-equilateral triangle for short.
These are commonly called by other names which refer specifically to the degree measure of their angles, but it is much better to call them by these names for two reasons (at least):
• Later we will use the radian measure of the angles, so we do not want to tie ourselves too much to degree measure
• The names given above remind us of what these triangles really are, so that we can recreate them if we forget the relationships of their sides, for example.
Important versions of the two special triangles: when the hypotenuse is 1.
You can see these two right triangles on this blog post from squarerootofnegativeoneteachmath (which also shows how they are used in the unit circle definitions of the trig functions, which we will discuss next time).
Embedding a right triangle in the coordinate plane:
We pick out one of the acute angles in the right triangle: let’s call it angle 
We are going to use this embedding to extend the definitions of the trig functions to angles which are not acute angles, so they are not angles of right triangles.
Homework:
• Review the isosceles right triangles and how we found the length of the hypotenuse using the Pythagorean Theorem, and also the half-equilateral right triangle and how we found its height using the Pythagorean Theorem. If you do this a few times, you will end up memorizing the triangle! You must learn it by heart as we will use it (and the other special right triangle) a lot in Trigonometry. Here is a good web source that shows how these triangles were developed. (Do not get too attached to the degree-measure names, though!)
Here is another good source on the half-equilateral triangle. (This one was also linked above in the notes.)
• Please note that we will be working from the Trigonometry textbook for most of the remainder of the semester.
Remember that you can use the Piazza discussion board to ask questions if you get stuck on any of the WeBWorK or the other homework problems. Don’t forget to include the problem itself in your question, as that will make it easier for you to get a quick response!
