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Since Rsin(x+y)=Rsin(x)cos(y)+Rsin(y)cos(x), we can set Rcos(y)=4 (1) and Rsin(y)=3 (2) on comparison to the desired equation. Considering (2) divided by (1) we see that tan(y)=sin(y)/cos(y)=3/4 so y=atan...

The answer to this question depends on one thing, whether this power is odd or even.

For even powers we use the identity cos(2x) = 2cos^2(x)-1 = 1-2sin^2(x). So for example, the integral of cos^2(x...

dy/dx = 3x+1/ -2y-3x-1

Not all matrices can be multiplied together, so the first thing to do is check it's even possible! To do this write the matrices next to each other (we'll call the first one A and the second B). If the nu...