Award-Winning Trigonometry Tutors serving Cambridge

The student and I spent the first half of the session going over his homework, which was to graph various sine and cosine functions, and identify the graphs of non-sine/cosine functions. Graphing sine and cosine were mostly easy for him, though he had a couple questions about trickier functions. For the second half, I explicitly defined some trigonometric identities (reciprocals, quotients, and negative angles), most of which he had already seen informally. As an exercise, I left him with the problem of trying to prove the Pythagorean Identity, the only identity I introduced that he hadn't previously seen.

The student and I continued practicing solving trig equations, slowly increasing the problems in difficulty. The student showed definite improvement, not just with the trigonometric processes, but also with the algebraic ones.

The student and I went over the general equation for the sine function. We talked about amplitude, period, phase shift, and vertical shift. I showed her how to graph equations on her calculator including using the trace and table functions.

The student is back from a break and this was our first session back. We moved ahead in the trigonometry book, and worked more on law of sines and cosines, as well as wave functions and their different parts. It went really well. I didn't see any scores/grades, but he did complete the assignments I gave him for our break, and he only had two questions. No struggles. I left him with three sections of homework for next week.

Today we began reviewing material that will be covered over the upcoming school year. We went over laws of exponents. This included numbers to the first and zero powers, multiplying numbers with exponents, dividing numbers with exponents, raising an exponent to a power, distributing exponents to an expression in parenthesis, and negative exponents. We completed example problems to demonstrate these laws.

We covered bearing/azimuth in terms of trigonometry. The student was very focused and attentive. She was much more familiar with using trig functions and finding angles (essentially seemed more comfortable with trig in general). I reviewed the material from her class, and then we went on to discuss homework. We reviewed one of each type of question, and I left her with the task of doing the rest of her homework by herself. We also previewed the Law of Sines and Law of Cosines. She grasped the material very quickly.