# Thread: It cant get easier than this ...

1. ## It cant get easier than this ...

Hello,

A question says solve $sin(x)=-sqrt(3)/2$ with no definite domain

Now I know how simple this is ..
But in class the teacher started explaining some weird stuff I couldnt understand.

Anyway, I know that I do : $arcsin(-sqrt(3)/2)$
ill get $x=-60$

now arent I supposed to do the following ? :
$
180-(-60)= 240$

So the solutions are $-60 +2(pi)n ; n= +/- 1 +/- 2 +/- 3 ....$
and $240 +2(pi)n ; n= +/- 1 +/- 2 +/- 3 ....$

Is the answer correct ? or am I doing something wrong :S

My teacher presented positive answers (+60) and not -60..
and in Wolfram Alpha, the answers are 120 and 60 ..

Thanks !!

2. Originally Posted by ZaZu
Hello,

A question says solve $sin(x)=-sqrt(3)/2$ with no definite domain

Now I know how simple this is ..
But in class the teacher started explaining some weird stuff I couldnt understand.

Anyway, I know that I do : $arcsin(-sqrt(3)/2)$
ill get $x=-60$

now arent I supposed to do the following ? :
$
180-(-60)= 240$

So the solutions are $-60 +2(pi)n ; n= +/- 1 +/- 2 +/- 3 ....$
and $240 +2(pi)n ; n= +/- 1 +/- 2 +/- 3 ....$

Is the answer correct ? or am I doing something wrong :S

My teacher presented positive answers (+60) and not -60..
and in Wolfram Alpha, the answers are 120 and 60 ..

Thanks !!
your answers and work are fine. it only depends on the domain. if no domain has been given then just provide a general solution like you have done above.

But the teacher says he wants the answers to be like his :S

Why does he get positive values ?

4. Originally Posted by ZaZu
and in Wolfram Alpha, the answers are 120 and 60 ..
Not for me they aren't

CB

5. UPDATE

Ok so I found out that there are both "Solutions" and "Elementary Solutions" in Wolfram Alpha.

So

Elementary solutions : x = -pi/3 = -60

But what are " Solutions" for ?

x = 2/3 (3 pi n+2 pi) =240, n element Z

x = 1/3 (6 pi n-pi) =-60, n element Z

Well anyway I got the 2 solutions correct, which is -60 and 240 ..

Dont know where I went wrong ..

I guess problem is solved then Im correct