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Session Summaries by Trigonometry Tutors

Trigonometry Tutoring review by Jerilynn in Provo, UT
We focused on reviewing the various theorems for determining the roots of a polynomial function. We practiced finding all the possible rational roots and determining which ones are actual roots. We talked about how to determine the number of complex roots of a polynomial and what the graphs look like if there are repeated roots. We went through creating a polynomial with specific roots, including irrational roots and complex roots. Lastly, we looked at how to determine how many positive/negative real solutions and imaginary solutions a polynomial could have. The student is doing well using the rational roots theorem to find the first few roots and reduce a polynomial down to a quadratic function. She is also doing better at determining the possible numbers of real and imaginary solutions a polynomial could have as well as working backwards from a set of given solutions to the least degree polynomial that corresponds.
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Trigonometry Tutoring review by Garrett in Provo, UT
Covered more strategies for proving equalities of trigonometric expressions. Worked closer with the double-angle formula. Explanation and practice with parametric equations. The student understands concepts well; she just needs to take each problem bit by bit and utilize strategies of algebraic simplification (at least for the trig expressions). Strategies include converting all terms into sines and cosines, expanding out multiplication expressions when useful (but factoring when there is a convenient cancellation that can be made), and switching back and forth between the left and right sides of the equality when one becomes stuck. If at any point it seems one can't move further, quickly check the table of identities and see if there's a useful substitution! And for parametric expressions with sines and cosines, don't be afraid to try summing the squares of x and y to see what happens! Most things lead back to the Pythagorean identity.
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Trigonometry Tutoring review by Michael in Provo, UT
Today, we worked on a project for the student's math class. The main point of it was to use two formulas to figure out the number of moves it would take to move 64 discs from one pile to another, given that only three piles can be in play at once and only one disc can be moved at a time, and a disc can never be placed on top of a smaller disc (the discs are originally stacked with largest at the bottom, smallest at the top). We eventually determined that the entire task, also called Tower of Hanoi, would in theory take billions of years to complete. We filled in much of a table that defined the minimum number of moves required to complete the puzzle at different numbers of discs, seeing that it increased greatly with each added disc. We established two formulas -- one based simply on the number of disc, and one based on the previous number of moves within the table. We then began writing out the process, as per her assignment.
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Trigonometry Tutoring review by Emily in Provo, UT
We reviewed past quizzes on the law of sines and cosines and went over some worksheets to study for tomorrow's exam. The student is doing very well with the material. Practice with drawing diagrams will be helpful. She needs to remember the area of a triangle formula with sine and how that relates to the standard 1/2*base*height formula. This understanding came up in a part of a word problem, so it is not huge but still relevant.
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Trigonometry Tutoring review by Robert in Provo, UT
I had a good session with the student today. We did test corrections from a recent test. He understood every problem. It's too bad we didn't go over the material before the test because he is very capable of doing the work. He was focused and easy to help.
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Trigonometry Tutoring review by Miguel in Provo, UT
I assisted in helping the student understand logarithmic expressions and how they are solved, exponential growth and decay functions, and word problems involving inverse functions. He was struggling with understanding how to find the inverse of a function. I explained thoroughly how to approach this step by step, and he eventually understood the concept.
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