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: Another Trigonometric Equation

  1. Oct 17, 2009 #1
    1. The problem statement, all variables and given/known data

    Solve for t


    2. Relevant equations

    Sum and Difference Identities

    3. The attempt at a solution

    I saw this problem the the sum identity sin([itex]\alpha[/itex]+[tex]\beta[/tex]) looked like the way to begin solving for t.

    This condenses to sin(3t+t)= -1/2 which is sin(4t)= -1/2

    I let 4t=x and now have sin x= -1/2

    The answers for this are 7[itex]\pi[/itex]/6+2[itex]\pi[/itex]n and 11[itex]\pi[/itex]+2[itex]\pi[/itex]n.

    This means that 4t equals both 7[itex]\pi[/itex]/6+2[itex]\pi[/itex]n and 11[itex]\pi[/itex]+2[itex]\pi[/itex]n. I need to divide the four out to get t by itself.

    The general solutions (I think) are t=7[itex]\pi[/itex]/24+[itex]\pi[/itex]n/2 and 11[itex]\pi[/itex]/6+[itex]\pi[/itex]n/2.

    Did I miss anything or does this look correct?

  2. jcsd
  3. Oct 17, 2009 #2


    Staff: Mentor

    In the next couple of lines, the 2nd expression should be 11[itex]\pi[/itex]/6 +2[itex]\pi[/itex]n, which it appears you caught later.
    In the next line, you got the "divided by 6" back in the second expression, but forgot to divide by 4.
    Make the above t=7[itex]\pi[/itex]/24+[itex]\pi[/itex]n/2 and 11[itex]\pi[/itex]/24+[itex]\pi[/itex]n/2.
  4. Oct 17, 2009 #3
    You're right. I had that written on my paper, but it's a typo here on the board. Thank you for reading my post!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook