Rotation of Axes Question

[FabZeros]

How do we decide whether cos2a or sin2a is negative if cot2a is negative? Sorry if I'm not being explicit enough...

 

[pka]

How do we decide whether cos2a or sin2a is negative if cot2a is negative?

I find this a very strange question. If you know the 'size' of a then surely you know the 'size of 2a .
Given the 'size' of a number you are expected to know the signs of the trig functions of.2a,

 

[Ishuda]

How do we decide whether cos2a or sin2a is negative if cot2a is negative? Sorry if I'm not being explicit enough...

You can't if all you have is cot(2a) is negative. In the image you have more information that that but only because "The following figure shows the second quadrant angle."

 

[FabZeros]

Ah so it doesn't matter when I use the power reducing identity to turn cos2a to cosa? Or just assume that it is in quadrant 2 just like how we'd assume a positive cot(a) would be in quadrant 1?

 

[Ishuda]

Ah so it doesn't matter when I use the power reducing identity to turn cos2a to cosa? Or just assume that it is in quadrant 2 just like how we'd assume a positive cot(a) would be in quadrant 1?

Well actually, I had rather do it the way presented here
http://mathworld.wolfram.com/QuadraticCurve.html
But, yes, you can use the reduction formula.

 

[FabZeros]

Thanks! I'll go over the link right now... It's really different from what I'm used to but I'll try to get it.