Comparison of Law of Cosines, Law of Sines and Pythagorean Theorem

The law of cosines, law of sines and Pythagorean theorem are all very important parts of trigonometry. Firstly the Pythagorean theorem is very useful when finding the sides of a right triangle. All it takes is squaring side c and setting it equal to the sum of the squares of side a and b. The law of cosines is simply an extension of the Pythagorean theorem, this takes the Pythagorean theorem and subtracts 2(a)(b)cos(C) from the equation. This is very helpful when working with SAS and SSS triangles. When using the Law of cosines the triangle that you are using does not have to be a right triangle and also allows you to use an angle of the triangle to assist in finding its values. The Law of Sines is very helpful when working with AAS and ASA triangles because to use this you need two angles. All of these Laws and theorems are intertwined like a well oiled machine, and without one the whole machine will stop working.

The graduation speech

 Dr. Stefano Bertozzi's speech talked a lot about how you shouldn't eat more than you bring, which is a very good mantra for everyday life.  In this speech he talked about how many people do more bad than they do good in the world, which is not a good way to lead your life. By exemplifying the idea that if you give as much as, or more than you take, yours and everyone else's lives will become more balanced. I really like the idea that you should be giving more to the world through doing good things and being kind to people than you are taking from it. Dr. Bertozzi's whole talk was very inspirational and well said. It left the audience to think about whether their affect on the world will be a positive or negative one.  This speech affected my way of thinking about each thing that I do and how I will be able to balance it out. Overall Dr. Bertozzi does a great job in helping everyone to think about giving their kindness and adding to the world instead of taking from it without contributing anything to the metaphorical pot luck.