Math Is Fun Forum

Edited my erroneous point coordinate. : facepalm:

In reference to 225

In my working out of x and y (x=4/5 and y=-3/5) which established an angle of -36.87 (or 323.13). These values for x and y and the angle satisfied both equations. ie
sin(-36.87)+2cos(-36.87)=1 and then 2sin(-36.87)-cos(-36.87)= -2 (and of course using 323.13 is the same)

I followed your working out and didn’t see an immediate error. The only thing that I can think of is that maybe the assumption that the root in last step is a positive 2 may be the issue. What I mean is that perhaps there was a positive and negative root and that the positive root was extraneous for reasons not immediately obvious through purely trigonomic substitutions. I am not sure, but my alternate solution still satisfied the first equation. To flip the sign to positive from what I found there has to be an angle in the first or third quadrant that would produce a positive 2. I had no luck finding that alternative angle that still satisfied the first equation.

No need to apologize, I still enjoyed working the problem as it was.