Today JPaul and I completed the practice test. We discussed graphs of trig functions, how to evaluate trig functions using the unit circle, the relationships between trig functions and their coterminal angles. JPaul will study the review tonight to be ready for his test tomorrow.
Today, we used the Unit Circle to derive the graph of tangent. We discussed that at locations of multiples of pi/2, tangent is undefined there. So on the graph there would be vertical asymptotes there. Then, we discussed how tangent can be transformed and how the period and phase shift could be affected. JPaul had some difficulty with setting up the x-axis. He will get better with more practice.
Today we used the dry erase board to compare the graphs of sine and cosine. We discussed how cosine can be determined using the unit circle, or by shifting the Sine graph left pi/2 units. I gave JPaul “what if” scenarios to test his understanding of stretching/shrinking/shifting/reflecting. JPaul showed mastery on this content. He understanding this material extremely fast. We then introduced phase shift, which proved to be a bit of a challenge. JPaul prefers to do calculations in his head, but will have to get comfortable writing it down so he can analyze properly.
Today JPaul was not himself. He told me that at 11PM he took NyQuil and he still felt groggy from it. We were supposed to have a quiz today, however I didn’t feel it would be JPaul’s best performance, so we are pushing it back to tomorrow. Instead, we did review problems that will be similar to the quiz. JPaul worked through them, he was slow to get started and unsure of himself. With some reminders, he was able to complete them.
Today we practiced evaluating all 6 trig functions, at various locations in the unit circle. JPaul did excellent. As a matter of fact, I don’t think I’ve ever had a student pick up so quickly on this content. We worked with radians and degrees. JPaul showed that given one angle and one side of a triangle, trig can be used to find the remaining sides and angles. Monday he will have a quiz on this content.
JPaul completed his poster of the Unit Circle. He labeled the degrees, radians, and ordered pairs of the appropriate locations. Then we discussed the relationship between sine, cosine, and tangent, to the unit circle. We practiced evaluating trig functions using the unit circle as an aid. Then we practiced evaluating trig functions without the unit circle (having to visualize it on our own). JPaul is understanding this material easily.
Today we reviewed the six trig functions and the relationship between them. For the next few days we will be pausing from the textbook to create a unit circle. We got a protractor and compass and JPaul created a circle. Then he labeled points on the coordinate plane that are 30, 45, and 60 degrees from the x axis. Tomorrow we will label these points in radians and discuss the relationship between each trig function and the points around the unit circle.
JPaul is whizzing through this new material on Trig!! Today we discussed the 6 trig functions and how we can relate them to triangles on the coordinate plane. We introduced new vocab, such as initial side, terminal side, and reference angle. For each new topic we discussed, JPaul practiced a problem. He easily understood the new content. We had some time left in class, so JPaul started on his homework independently.
