simplify trig (sinx-kcosx)/(cosx+ksinx), k=constant

dagr8est

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Nov 2, 2004
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This is actually for a physics problem and there may not be a way to simplify it. I was just wondering if anyone saw a way to simplify it so my solution would look nicer. Any help is appreciated. :D

(sinx-kcosx)/(cosx+ksinx) where k is a constant
 
dagr8est said:
This is actually for a physics problem and there may not be a way to simplify it. I was just wondering if anyone saw a way to simplify it so my solution would look nicer. Any help is appreciated. :D

(sinx-kcosx)/(cosx+ksinx) where k is a constant

sin(x)kcos(x)cos(x)+ksin(x)=tan(xθ)\displaystyle \frac{\sin(x)-k\cos(x)}{\cos(x)+k\sin(x)}=\tan(x-\theta)

where

θ=arctan(k)\displaystyle \theta=\arctan(k)
 
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