Friday, April 2, 2010

We spent a good deal of class working on the warmup problems. Basically, it was the application of the Fundamental Trigonometric Identities. The primary benefit of the exercise was that it gave us a chance on making our proof format more acceptable. Format work included using the equals sign in a transitive manner, and making sure everything was thoroughly explained. If you’re not evidently applying a property, it’s best to leave a side note for thorough explanation. For example,

If cotx + csc= cos/(sin^2), you couldn’t make the leap to “cos/(sin^2)=cos/(sin^2)” without first explaining your manipulation of cotx and cscx.

On concept that came up several times throughout the warm-up was the technique of multiplying by fufoos to get lowest common denominator. This can be particularly useful with complicated fractions.

After we had learned to write proofs in a more explanatory manner, we started work on the homework problems.
While working on the homework, there was some reviewing of how to derive the other pythagorean identities. For those who need a reminder, just divide the values on both sides by (sin^2)x or (cos^2)x. Basically, working on the homework solidified strategies we had previously gone over, like multiplying by fufoos.

Then, we worked on Solving Trig Functions. Instead of trial and error, we worked with technology to solve the equations. Note that some of the solutions to these trig functions looked similar to the format used in our Francois worksheet.

At the end of the class, we briefly talked about future algebraic solving.