December 13th, 2016, 06:59 PM  #1 
Newbie Joined: Dec 2016 From: Natal  Brazil Posts: 10 Thanks: 0  Plane Coordinates
The attached figure illustrates a rectangular coordinate system xy generated by the unit vectors of the canonical base $\displaystyle \vec{i}$ and $\displaystyle \vec{j}$ and a system of coordinates nonrectangular $\displaystyle {x}'{y}'$ generated by the unit vectors $\displaystyle \vec{u}$ and $\displaystyle \vec{v}$ ($\displaystyle \left \ \vec{u} \right \ = \left \ \vec{v} \right \ = 1$), where the axis $\displaystyle {y}'$ coincides with the yaxis, while $\displaystyle {x}'$ is obtained from its anticlockwise rotation by an angle $\displaystyle \theta = \frac{\pi}{6}$. Find the $\displaystyle {x}'{y}'$ coordinates of the points whose coordinates $\displaystyle xy$ are $\displaystyle (10,3)$. Use $\displaystyle cos(\frac{\pi}{6}) = \frac{\sqrt{3}}{2}$ and $\displaystyle sin(\frac{\pi}{6}) = \frac{1}{2}$.( Remember that $\displaystyle (x,y) = x\vec{i}+y\vec{j} = {x}'\vec{u}+{y}'\vec{v}$)

December 13th, 2016, 08:15 PM  #2  
Math Team Joined: May 2013 From: The Astral plane Posts: 1,592 Thanks: 620 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan  
December 14th, 2016, 02:01 AM  #3 
Newbie Joined: Dec 2016 From: Natal  Brazil Posts: 10 Thanks: 0  
December 14th, 2016, 04:57 AM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,723 Thanks: 700 
Seeing that this involves angles and you get coordinates of a points in a given coordinate system by drawing perpendiculars from the point to the coordinate axes, I would start by drawing those lines and using trigonometry. (Do you suppose that's why they gave you the sine and cosine of $\displaystyle \pi/6$?)


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