# Math Terminology: “Find all solutions” = “Solve the equation on interval 0 < x < 2π”

Suppose the following question:
"Solve the equation sin(3x) = -1/2 on the interval 0 < x < 2π"

Would you interpret the question as meaning:
"Simply Solve the equation on the given interval (which would be 7π/18, 11π/18)"

-OR-

Would you interpret the question as meaning:
"List all of the possible solutions to this equation on the given interval (which would be 7π/18, 11π/18, 19π/18, 23π/18, 31π/18, & 35π/18)"

My interpretation of the question is to simply solve it, since that is what it literally states. Perhaps my understanding of the meaning of "Solve" is incorrect, because what the question really wanted was "All possible solutions".

Could you please give your insight as to whether my understanding of "Solve" is incorrect, or the wording of the math problem is incorrect.

-
If you have an incomplete solution, you haven't really solved it yet have you? At least that's how I see it... – Nicolás Kim Nov 27 '12 at 6:15
My interpretation is get all solutions. Suppose I asked you to solve $(x-3)(x-5)=0$. Would $x=3$ be a full answer? – André Nicolas Nov 27 '12 at 6:17
If I asked you to solve the problem of world hunger, would you have a cheeseburger and declare success? – Gerry Myerson Nov 27 '12 at 6:19
I don't understand why you say "which would be $7\pi/18$, $11\pi/18$" -- why would it be that? Why two solutions and not just one, and why these two? – joriki Nov 27 '12 at 7:28
The two answers you give are the ones you get with the restriction $0\lt3x\lt2\pi$ --- but that's not the restriction as stated in the problem. – Gerry Myerson Nov 27 '12 at 12:31