Trig
posted by Kate on .
I was doing this problem
sin^1 (4/5) if I'm not mistaking most teachers would say that .927295218 radians is wrong is just an estimation and therefore is wrong so I'm justified in putting this on my paper instead right
( ln( (4i +3)/5)/i )
right? She couldn't mark that wrong... if anythign she should mark .927295218 wrong because it's only an estimation much like using 3.14 for pi
now my question is do I need to show how I got that? Do I need to put the formula... I'm kind of confused by this because if it was sin^1(1/2) and I just put pi/6 down and didn't show how I got it most teachers wouldn't mark that wrong no...
So am I justified in just putting my answer down or not... if not why... There's no real work to be shown it's just some formula... much like F=ma but in math if I'm not mistaken you don't have to put the formulas like most teachers in math don't require you to put the quadratic equation down on an assignment and then do the work you can show the work if you can't do it in your head but if you can do it in your head most taechers I find with that right...
The only reason why I don't want to show my work is because the teacher gave us boxes to put are work in and the box for that problem is like an inch wide and .5 an inch tall not enough room to put all of my work and I didn't want to write stuff in the margins... plus no real work needs to be shown it's just some simple formula that can be found after doing the work...
If you were my tacher and I just put that down in the box would you take any points off? I don't see how becaues if the problem was sin^1(1/2) and I just put down pi/6 it would be fine so...

e^{ix}= cos x + i sin x
e^ix = 3/5+ 4i/5
ix= 1/5 (3+4i)
x= (3+4i)/5i
Now I don't know exactly what the teacher asked, did she ask for the angle, or not. Few folks would call this an angle. Depending on what I had taught in class, I probably would have counted both correct, but jotted a note on your answer "cute". Actually, I would have specified "answer in radians" on the question.
So on both counts, technially, you are correct: the first is an estimation, the second is "exact" in the DeMor 
Oops, sent before I was through. The right hand side should be obviously ln((3+4i)/5i), and DeMor should be de Moivre's complex plane representation.

My instructions were just to "Evaluate" why is that not considered an angle?

I thought that this was already in radians by the way...
ln( (4i +3)/5)/i
why is it not considered to be in radians? 
evaluate: Then both are right.
ln((3+4i)/5i) is a representation of an angle, however, it is not commonly used in angle measurement. Again, I would have given it an OK.