Today JPaul and I built on the concepts we started yesterday. Using a given trig ratio and the sign of another, we first had to determine what quadrant our reference angle was in. Then we drew a triangle with the x axis and labeled the sides appropriately. To find the third side we used the pythagorean theorem. Then we used SOHCAHTOA to find all the remaining trig functions. This was a bit difficult at first. JPaul had to recall sine is y, cosine is x and tangent is y/x. He also had to rationalize the answers when they were not in simplest form. I guided him through the problems at first, but toward the end of the class he was able to do them correctly on his own.
Today we finished the AP PreCalc content! YAY! From here on out we will review every day. However, today's lesson we discussed rates of change in polar functions. We considered as we move around the unit circle, given the equation, what happens to the radius. Sometimes it is positive/negative, and increasing/decreasing. We were able to determine this using the polar graph, however, we realized if we drew the rectangular graph it was much easier to visualize since we could see if the graph was above or below the x axis and also if it was increasing or decreasing. Josh did well with this last concept!
Richard took his spelling test and wrote the sentences I dictated to him. Using letter tiles, I showed him words with mis, post, and non prefixes to read. He read books with words he can read.