Recent Tutoring Session Reviews
"Yesterday the student and I went over a take home packet she had covering trigonometric identities. Specifically we were trying to prove that one side of an equation was equal to another. Overall it went well. She also had a test the following day so we made sure to review for that as well. It seemed to me that she needs help with her algebra skills so this is something we will focus on in the future."
"The student and I reviewed her trigonometry homework packet. She felt that she did not understand concepts so far, and I checked the work she had done and asked her to summarize her methods. Most used good logical reasoning, and where others did not, I used inquiry to guide her to rework them. She was quickly solving problems using the three main trigonometric functions (sine, cosine and tangent) and we were able to progress to more complicated word problems. Her largest difficulty was setting up the diagram to begin applying the trigonometric functions to solve for angles and sides. By the end of the session, she was highly adept at using the specialized functions in all cases. She told me by the end that she was much more confident and now understood the concepts and use of the math."
"We went over basic triangle properties (Pythagorean theorem). We defined sine, cosine and tangent (soh cah toa) and did some problems using the formulas. We also looked at the unit circle and determined radian units for angles. We started finding the cos and sin of standard angles (0,90,180 degrees). We discussed the coordinate system using degree/minute/second. I left him some problems to work on concepts we went over. Next time we will do coordinate problems and get into cos and sin of more standard angles on the unit circle, and into more properties concerning these."
"The student and I worked through her trigonometry packet to prepare for her test. She was having the most difficulty determining unknown side lengths of similar right triangles. I explained the different tools she could use to solve the problems and how to organize her work. I also reexplained some patterns that she should memorize ('boomerang' and 'heartbeat'). She was also having some difficulty completing application problems that incorporated two triangles. We worked through a few practice problems and I explained how to solve equations with more than one unknown variable. At the end of the session she took a practice quiz which she did very well on. I encouraged her to look over the problems she got wrong and redo them without looking at her notes."
"We specifically went over vectors and their applications. The student knows the material but needs help applying it. I told him that things he learned from the previous months will help him solve the problems that he is having trouble right now. Overall, the session was excellent."
"We again worked on multiple subjects. We had a brief English vocabulary lesson based on context clues. The new chapter in math introduced polar coordinates (r, theta). R is the length or distance from the origin or polar vertex to a discreet point. Theta correlates to the angle at which the point is oriented from the origin. The polar coordinates can also describe a line that passes r and -r distance through the origin. These coordinates can be expressed in positive and negative values to the r and -r positioned lines. A third coordinate can be given for moving the positive direction (counterclockwise) to the -r value (past the r value). To give all polar coordinates is to give 3 polar coordinates."
"We went over homework problems involving the law of sines, the law of cosines, and the ambiguous case. We also went over how to find the area of a triangle using the law of sines. By the end of the session, she was able to solve the problems correctly."
"The student has begun the trigonometry chapter, working on section 10.1, which covered conversions from radians to degrees and vice versa, as well as section 10.2, which reviewed the trigonometric identities and practiced finding the remaining trigonometric identities given information about one of them. He had no trouble with this homework."
"We covered a couple of sections from chapter 8 of the book. He was mostly struggling with Laws of Cosine and Complex numbers. He understood most of the section we covered."
"Today was all about trig fundamentals. We broke down sin and cos and what they are geometrically and it turns out that he was asked to memorize special angles and their evaluations. He has a test tomorrow, so this is likely our only session, but he says he feels more comfortable with the material now than before, and it seemed like that was true from his progress over the course of the lesson."
"In today's session, we discussed coterminal angles and converting angles from radians to degrees. I showed him an simple, structured way of doing unit conversions, which he can apply to science as well as math. I gave him a homework assignment to become familiar with and eventually memorize sin, cos, and tan of 30, 45, and 60 (also in radians). He was quick to understand conversions, but we will need to continue our next session by revisiting coterminal angles."
"We worked on proving various trig functions using Pythagorean, reciprocal, quotient, and even-odd identities. The process to solve each problem also used many Algebra properties including factoring, conjugations, and faction multiplication/ division. The student did a great job working through each problem and he used good logic to obtain the solution. For additional practice I asked that he work through the remaining problems dealing with exercises. The student scored a 100 on his exam from the previous week. The exam covered identifying the amplitude, phase shift, and period of trig equations and graphing trig functions from a given equation."