1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Solving Trigonometric Equations

  1. Nov 16, 2011 #1
    1. The problem statement, all variables and given/known data


    2. Relevant equations

    3. The attempt at a solution



    So here's my problem. Should it be positive or negative? Or just positive? Since the square root of any positive number can be positive or negative, right? Is there a possibility that the answer can be both positive and negative?


    if so, [itex]\Theta=45 degrees[/itex] [itex] or[/itex] [itex] 135 degrees[/itex] ---- for positive value of [itex]sin\Theta[/itex]

    [itex]\Theta=-45 degrees[/itex] [itex] or [/itex] [itex]315 degrees[/itex] [itex] or[/itex] [itex] 225 degrees[/itex] ---- for negative value of [itex]sin\Theta[/itex]

    So, I'm confused if:




    Can be:




    So can it be?
    Is it mathematically correct to think of it that way? Sorry if this is such a stu*id question. :)
    Hope you can help me! :)
  2. jcsd
  3. Nov 16, 2011 #2


    User Avatar
    Gold Member

    [itex]\sqrt{2}[/itex] is positive and separate from its negative counterpart, [itex]-\sqrt{2}[/itex]. If the question did not say [itex]± \sqrt{2}[/itex], then you can safely just worry about the positive value.

    If, on the other hand, the question was [itex]4sin^2 \Theta-2=0[/itex], then when you take the square root you must be sure to include the ±.

    It is sort of like saying [itex]x=\sqrt{25}[/itex] is equal to positive 5 only, however if i said that [itex]x^2=25[/itex], then x could be +5 or -5.
  4. Nov 16, 2011 #3
    Thank you for clearing this out for me!
    Sadly that was on my quiz and I totally included the negative root as a solution for the equation. :(

    At least now I know it. Thanks for answering! :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook