Hello everyone, this is my first post here and I am very glad to have discovered this forum. I will try very hard to get the Latex correct, but please forgive me if I mess something up.
I am very stuck on the following question.
This is how I have tried to solve it using Trig identities.
I have a hunch that I should just stop here, because I can tell I've done something wrong. I would continue on trying to find sin=1 and cos=1, but it just doesn't work.
Any help that can be offered would be greatly appreciated. Also, \\ isn't giving me a new line in latex. Perhaps I am missing something there?
Mar 12th 2011, 08:12 PM
My mistake, I believe that should be .
It is still getting me into the same place though.
Mar 12th 2011, 08:20 PM
Assuming that values of that make are not possible solutions (I'll leave you to check this)
Go from here...
Mar 12th 2011, 08:21 PM
try to do it like this:
find x by using calculator
multiply the whole equation by sinx
can u take it from here..(Wink)
Mar 12th 2011, 08:33 PM
Wow, thank you both for the very quick answer. Looking at that now it seems obvious, however I have one small hang-up in the directions of my textbook, and I am not quite sure what it means. It reads like this.
"In algebraic equations, we generally do not divide each side by any expression that involves a variable, and the same rule holds for trigonometric equations."
Because of that sentence (whatever that means) I haven't been cross dividing anything.
So if I follow the workings below,
Strange though, if that is the correct track. Every other answer has been giving me two answers. I suppose if I shifted that into quadrant 3 I would get 12.36.
Still on the right track?
Mar 12th 2011, 08:38 PM
There will be more than one answer...
Assuming you have used radians...
Since the tangent function is positive in the first and third quadrants, if then
, where is an integer.
Mar 12th 2011, 08:56 PM
Yes, I have used radians. One part of this problem that I forgot to mention is that it is in the interval [0,2╥), so I don't need +2k╥. Sorry, I should have mentioned that earlier.
I also noticed that I made an error in my last post. It should look like this.
This works when I plug it back in, so thank you very much. I was not able to get this far on my own. Taking it further, I suppose that I can find the other again within the interval by looking at the unit circle. Doing this I find that the other angle is approximately 3.30..
You guys rock.
Any advice on the // thing for spacing in Latex? I am doing it in sort of a long-about fashion. Which you can see if you look at my code.
Mar 12th 2011, 09:01 PM
You actually do need the , because if
It's quite possible that since the period is diminished, then there are more solutions in the interval.
Mar 12th 2011, 10:20 PM
Your completely right, I had forgotten about the half angle identity involved. Although it appears that these answers are only in quadrant 1 and 3, so they are already ╥ distance away from each other.