Joshua and I worked some more problems which could be solved by using the law of sines. I then reminded him of the law of cosines and showed him two examples of solving triangles using the law of cosines. There was one triangle with two sides and one angle given and one triangle with all three sides and no angles given. There was no assignment.

Matthew finished his test on rational exponents and radical expressions and scored 100%. We decided to continue on to the next unit of study and I opened the chapter with the growth of 1 penny doubled every day for 1 month. At the end of the month, the value reaches over ten million dollars. This enabled us to appreciate some of the features of the exponential growth curve. There was no assignment.

Joshua and I continued to work with triangles with zero, one, or two solutions. We used the height of the triangle to determine how many solutions there were. There was no assignment.

Matthew took a test today on rational exponents and radical expressions. The test included simplifying radicals or numbers raised to rational exponents. Some of the radical expressions included variables. The test also included compositions and other operations on functions as well as finding the inverses of functions. There were also two problems with radicals in equations that need to be solved and checked. There was no assignment.

I continued my instruction with Joshua to show how some triangles with given sides and angles would have no solution when one side was too short. Other triangles would have exactly one solution, and some triangles would have two solutions. I also showed him examples of using the law of sines to solve triangles. I instructed him to work on some guided practice problems. There was no assignment.

I finished reviewing how to simplify rational exponents and radical expressions with Matthew. We solved and checked equations involving rational exponents and radical expressions. We also found inverses of functions as well as adding, subtracting, multiplying, dividing, and applying composition of functions. In some problems it was necessary to list restrictions on the domains. There was no assignment.

I worked with Joshua to show how some triangles with given sides and angles would have no solution when one side was too short. Other triangles would have exactly one solution, and some triangles would have two solutions. I also showed him examples of using the law of sines to solve triangles. There was no assignment.

I continued to review with Matthew how to simplify rational exponents and radical expressions. We found inverses of functions as well as addition, subtraction, multiplication, division, and composition of functions. In some problems it was necessary to list restrictions on the domains. There was no assignment.

Joshua and I worked with given information and inverse trigonometric functions to find a missing angle when other parts of the triangle were given. We then started to use the law of sines which he had learned last year in geometry to solve for all of the sides and angles of triangles. We followed one example and did two guided practice problems. There was no assignment.

I instructed Joshua to provide the inverse trigonometric functions in either radians or degrees. Sometimes I provided the hypotenuse and one side, sometimes I didn't have to provide any information at all. We also found some angles which were not in the first quadrant. There was no assignment.