Topics:
More rationalizing denominators and complex numbers
• Trigonometry topic: special right triangles
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.
Trigonomety in 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.)
Here is the chapter from Prof. Africk’s textbook which discusses similar triangles: AfrickGeometryTexctbookSimilarTriangles
In addition to the WeBWorK, you should do problems 7 – 10 from p. 174 there. The answers will be posted here later.
