I showed Joshua how to translate the graphs of sine, cosine, and tangent of x both vertically and horizontally. I showed him how shifting the sine or cosine of x can change the sine of x to resemble the cosine of x or even the negative sine of x. I also showed him vertical transformations. There was no assignment.

I reviewed problems with Matthew about simplifying, multiplying, and dividing rational expressions. I then introduced the topic of adding and subtracting rational expressions with the same or different denominators. We looked at an example of how to find the least common multiple. There was no assignment.

I demonstrated to Joshua how to graph various trigonometric functions with different amplitudes and periods. I also showed him the tangent function graph with various amplitudes and periods. I pointed out that the tangent function has a period of pi instead of two pi. There was no assignment.

I worked with Matthew to practice problems involving simplifying, multiplying, and dividing rational functions. I mentioned to him that some fractions cannot be simplified and I reminded him that in division, he should always multiply by the reciprocal of the second function. We did several representative problems. There was no assignment.

I continued to teach Joshua how to graph the sine, cosine, and tangent functions against the angle measurements in radians. I was able to demonstrate to him how the period and amplitude are influenced by constants in the formulas. There was no assignment.

I administered the test on exponents and logarithms and began the next chapter on simplification and multiplication of rational functions. Matthew finished the test and scored 100%. The new chapter included cancelation of factors common to both the numerator and denominator of a fraction. There was no assignment.

I went over different techniques of solving logarithmic equations with Matthew including compacting and expanding logarithms to solve equations. I reminded him that the base of ln is e and the base of log is 10. We then did some chapter review problems to prepare him for the test. There was no assignment.

I worked with Joshua to identify specific parts of the sine and cosine curves. I demonstrated how the values of the functions increase and decrease between the minimum and maximum values at different parts of a period. We looked at an example of how to graph the functions. There was no assignment.

I gave Joshua his test on trigonometric ratios and functions to complete. It consisted of 16 questions including problems about the six trigonometric functions of triangles with two given sides, conversion of radians to degrees and degrees to radians, finding angles using inverse trigonometric functions, solving triangles, finding areas, and taking trigonometric functions of angles given as inverse trigonometric functions. Joshua finished the test and made a perfect score of 100%. There was no assignment.

I worked with Matthew on some practice problems to apply the properties of exponents and logarithms when solving equations. I indicated that one strategy was to find equal bases and equate the exponents. There was no assignment.