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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
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