AboutScotto Expertise Any kind of mathematics (algebra, geometry, trigonometry, matrices, calculus, linear approximation, linear regression, linear programming, numerical analysis, probability, statistics, etc.). I also have answered some questions in Physics, Chemistry, and Biology. I would like to volunteer in all areas of Mathematics, not just calculus, and the other three courses that were mentioned.
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.
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.
