Have you quoted the problem exactly right? Is there some region of interest, some interval in which you're looking for solutions? Are you sure it isn't
If , write the general solution for ?
Answer:If x=arcsinA=1 radian, write the general solution for arcsin A.
x=arcsinA=1
sin1=arcsinA
0.841471=A
arcsinA=1
How do I look? This seems like a shady question and there is no where to reference it in the text book...
Well, if arcsin(A) = 1, then it is not true that sin(1) = arcsin(A). It is true that A = sin(1).
The problem might be asking about how to find all the A's that satisfy the equation. In that case, you'd need to use the symmetries of the sine function to solve it. If you have quoted it 100% accurately, as you've claimed, then it is a terribly worded problem.
But that's life. Life throws all kinds of terribly worded problems your way. Part of problem-solving in the real world is to clarify the problem!
Believe it or not the following is a serious question.
Who uses degrees any more and then WHY?
I was at a technology conference some twenty years ago. I watched Ross Finney give a beautiful rant on this. His point was handheld devices should always be in number (read radian) mode.
Reply to Plato:
You can blame it on the engineers. They use degrees all over the place.
However, since engineers are often at least as smart and often more influential than mathematicians (for sheer numbers if for no other reason), there's a decent chance this won't change a whole lot in the near future. Also, degrees are used in navies for bearings in navigation.
I have no doubt that you are correct.
But Ross was at MIT. So his response is at the more curious.
In my own case, the university required an outside evaluator on a thesis defense.
The engineering school assigned their expert on integration.
My advisor told me to say up front, “the integral we investigate makes any derivative integrable”.
Well that did it. Those are the only words that I said. There in sued and hour of debate between the mathematics department and the socalled expert on integration from engineering.
Now to be honest: My PhD university is not known for engineering.
NO,
look at mine in which the first arcsin is replaced by Arcsin!
arcsin(x) means the set of all of the angles which their sine is equal to x.(the general solution)
But Arcsin(x) means the original angle whose sine is equal to x. (Infact -pi/2<=Arcsinx<=+pi/2).
Indeed, arcsin(x)=2k.pi+Arcsin(x) and arcsin(x)=2k.pi+pi-Arcsin(x)
Therefore if your book says mine, then the solution set is:
arcsine(A)=2k.pi+Arcsin(A) and arcsin(A)=2k.pi+pi-Arcsin(A)
And since 1 is in radian measure, then the solution set B is: B={2kpi+1 , 2(k+1)pi-1 : K is an element of Z}.