Hi guys, I am having a hard time understanding this particular problem I dont understand how the result is converted and handled in Pi format and why this does not happen when I have a square root. Any thoughts?
Could you be just a bit more specific? What do you mean "how the result is converted"? What do you mean by Pi format? Which square root are you talking about? And why what does not happen when you have one? Here's an idea. Show us YOUR best attempt at working these so that we can see what you are doing and that will probably let is spot where your confusion lies.
The problems are all solved. I am trying to figure out out why the result of some comes in Pi over something format. How do I get to that result.
Are you familiar with radians? It is a measure of angle in which the value is the ratio of the arclength subtended by an angle to the radius of that arc. There are 360 degrees in a full circle. There are 2pi radians in a full circle. There's not much else to it.
arg(z) is an angle. Therefore when you take the arctan of -1/1 (as in b), you get -pi/4 radians, or -45º. To convert radians to degrees, multiply by 180 and divide by pi. BTW, in c, it should really be arctan (1/-1), since it is y over x.
So you convert the (1/-1) to angle using tan-1 which gives -45º and since 2 pi = 360º I can say this is the same as -0.25 or -pi/4 Ok, that was simple and answered my question. Thanks! So what I need is to setup my calculator to display the result in fractional mode right? You are right about c I was looking at that before! Amazing teachers still have mistakes on the learning material even tough is the same every year...
There's nothing wrong with c. It doesn't matter if the numerator is chosen to be the negative (as long as the ratio's the right way round). If you know what quadrant (s) you're in you can omit the sign when computing the angle.
How can anything be -0.25 or -pi/4? This is like saying that the height of a building is same as 100ft or 314ft. -pi/4 is ~ -0.785. How is that the same as -0.25?
My problem with c is that they are inconsistent with their own notation when compared to d. In that case they explicitly indicate the sign of the numerator and denominator separately, so it is not unreasonable to expect them to be consistent and do that in c, as well.
Yes, I see what you mean now. If I could nit-pick, I would have gone for the principle-value range myself.
I generally use the atan2 concept of Atan(y,x) so that I can keep the quadrant information intact and track it as the work progresses. Then, at whatever point is necessary, you can consider the quadrant implications of the various terms.
atan2() is a function (not always called that, but more often than not) than most computer language libraries support that return the four-quadrant arctangent of an angle. To do that, you give the y and x coordinates separately so that it can detrmine what quadrant the angle is in. If a particular language doesn't support atan2(), it is trivial to write your own using just the normal atan() function.