AboutScotto Expertise Any kind of mathematics (calculus, analysis, game theory, linear approximation, finite differences, linear regression, linear programming, numerical analysis, probability, statistics, etc.).
I also have answered some questions in
Physics (mass, momentum, falling bodies),
Chemistry (charge, reactions, symbols, molecules), and
Biology.
Experience Experience in the area: I have tutored students in all areas of mathematics for over 20 years.
Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors.
Awards and Honors: I have passed Actuarial tests 100, 110, and 135.
Publications Maybe not a publication, but I have respond to well oveer 3000 questions on the PC.
That's around 2,000 in basic math and 1,000 in advanced math.
Education/Credentials I aquired well over 40 hours of upper division courses. This was well over the number that were required.
I graduated with honors in both my BS and MS degree from Oregon State University.
I was allowed to jump into a few junior level courses my sophomore year.
Awards and Honors I have been nominated as the expert of the month several times.
All of my scores right now are at least a 9.8 average (out of 10).
Past/Present Clients My past clients have been students at OSU, students at the college in South Seattle,
referals from a company, friends and aquantenances, people from my church, and people like you.
Question please give me the proof of the equation Cos2X+Cos2Y+Cos2Z=1
Answer This is just like a three dimensional triangle.
The Pythagorean theorem states that a²+b²=c² when in two dimensions. Divide the entire equation by the variable c to get
(a/c)²+(b/c)²=1. Note that a/c=cos(t) and b/c=cos(u) where u and t are the two angles in the triangle.
The equation is then cos²(t)+cos²(u)=1 for all u,t where u+t=90.
Take a three dimesional box with sides w, l, and h.
The diagonal across the bottom²=w²+l². This diagonal line we will call d. It is alson known that d²+h²=c² where c is the line across the recangular box from the lower corner to the opposite top corner.
We know that d²=w²+l², so putting this in gives w²+l²+j²=c². Divide the entire equation by c² and you will get the equation given. That is, the sum of cos² of each of the angles is 1.
