November 24th, 2017, 05:47 PM  #1 
Newbie Joined: Nov 2017 From: Brazil Posts: 1 Thanks: 0  Learning analytic geometry
Hi, I study alone and I'm having difficulties with these issues, please help me! Questions: 1 Determine which type of central grid is from its curves. (x ^ 2) / (a ^ 2) + (y ^ 2) / (b ^ 2)  (z ^ 2) / (c ^ 2) = 1 2 Prove that rotations in R ^ 2 commute. Ra * Rb = Rb * Ra 3 Prove that roca in R ^ 3 do not commute. 4 How to transform cylindrical coordinates into Cartesian coordinates? 5 ρ sin ϕ = 2 A surface in R ^ 3 is given by coordinate (ρ, θ, ϕ), how to translate into Cartesian coordinates and what is this surface? Last edited by skipjack; November 24th, 2017 at 08:40 PM. 
November 29th, 2017, 04:11 AM  #2  
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902  Quote:
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Look at $\displaystyle \begin{bmatrix}cos(\theta) & sin(\theta) \\ sin(\theta) & cos(\theta)\end{bmatrix}\begin{bmatrix}cos(\phi) & sin(\phi) \\ sin(\phi) & cos(\phi)\end{bmatrix}$ and $\displaystyle \begin{bmatrix}cos(\phi) & sin(\phi) \\ sin(\phi) & cos(\phi)\end{bmatrix}\begin{bmatrix}cos(\theta) & sin(\theta) \\ sin(\theta) & cos(\theta)\end{bmatrix}$. Are they the same? Quote:
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