Determine the minimum and maximum points on a graph?
Y = 12cosθ - 5 sinθ with a range of 0 - 360°

So far I have got...

dy/dx = 12sinθ - 5cosθ

sinθ/cosθ = -12/-5 = 2.4

1st Quadrant = 2.4/Tan = Tan^-1 (2.4) = 67.38°

The problem is I understand 360° is within the 4th Quadrant however by just adding 360 to 67.38° I get 427.38° - this can't be right...can it? How do I calculate the 4th quadrant so that I can then calculate the min and max values...

Thanks alot for your help - from a very confused person

 

Thanks alot for your help - from a very confused person

Well, you aren't all that confused because you have it mostly correct.

There is a mistake in your dy/dx which should be -12cos-5sin, but you have the rest correct in principle. The only remaining thing is that arctan repeats every 180 deg, and not 360 deg. So just add 180 to your first answer to get the second answer.

If your calculator gives you a negative value from the arctan then just add 180 degrees to get it in the range of 0 to 180. I think the standard range of arctan is -90 to 90 deg, but this is kind of an arbitrary mathematical convention which gets overridden by the question which demands the answer in the range of 0 to 360 deg. So your initial answer should be shifted by 180 deg until it is in the range of 0 to 180, and then add 180 deg to that answer to get the second answer.

EDIT: I noticed another math error in your analysis. The final formula should be tan(x)=-5/12. So, you missed the sign and inverted the ratio. Instead of 12/5, it should be -5/12. But, you at least have most of the concepts down. We all make algebra mistakes like that.

 

Thanks a lot for your help - its nice to get a good explanatory answer that does not make me feel silly - thanks again