1. Not finding help here? Sign up for a free 30min 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!

Radian angle solving

  1. May 30, 2008 #1
    1. The problem statement, all variables and given/known data
    [tex]2sin(x-\frac{\pi}{3}) = 1[/tex]
    for the range 0 <= x<= 2π

    The attempt at a solution

    so [tex]x-\frac{\pi}{3} = \frac{\pi}{6}[/tex]

    i can get the first solution which is π/2 but how do i get the next solutions?

    Thank you
  2. jcsd
  3. May 30, 2008 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Examine the graph of a sine function between 0 and 2π. Find all angles where sine = 1/2. π/6 is only one of them.
  4. May 30, 2008 #3
    well there is 1 more in the range of 0 to π to 360

    that is π - π/6
    = 5π/6

    so the answer is

    π and 5π/6

    is there any more? i presume i dont count the -1/2s

    thanks :)
  5. May 30, 2008 #4

    Doc Al

    User Avatar

    Staff: Mentor

    Right. So the two values of [itex]\theta[/itex] that satisfy [itex]\sin\theta = 1/2[/itex] are [itex]\pi/6[/itex] & [itex]5\pi/6[/itex].

    Given that, what are the values for x?
  6. May 30, 2008 #5
    do you add π/3 to both of them?

  7. May 30, 2008 #6

    Doc Al

    User Avatar

    Staff: Mentor

  8. Jun 1, 2008 #7
    This is the way I was taught to do it :
    [tex]2\sin (x-\frac {\pi}{3})= 1[/tex]
    [tex]\sin (x-\frac {\pi}{3})= \frac {1} {2}[/tex]
    Let [tex]q =x-\frac {\pi}{3} [/tex]
    [tex]\sin (q)= \frac {1} {2}[/tex]
    Where is the [tex]\sin q = \frac {1}{2}[/tex] ?
    At [tex]\frac {\pi}{6}, \frac {5\pi }{6}[/tex]
    Thus : [tex]q_{1} =\frac {\pi}{6} , q_{2}=\frac {5\pi }{6}[/tex]
    We're not done. We still have to solve the x. Note that I was supposed to add 2 Pi to q 1 and q 2, but if you do it separately, you will see the solutions would not be needed since they are outside of 2 Pi when we add pi /3.
    Continuing : Simply setting the q's equal to x - pi /3
    [tex]x-\frac {\pi}{3} =\frac {\pi}{6}[/tex]
    [tex]x-\frac {\pi}{3} =\frac {5\pi }{6}[/tex]
    Solving, we get the solutions to be : [tex]x_{1} = \frac {\pi}{2},x_{2} = \frac {7\pi}{6},[/tex]

    In your calculator, if you graph these two functions, you will see the solutions to be those as noted.
  9. Jun 1, 2008 #8
    Thanks!!!! :)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Radian angle solving
  1. Solving Angles (Replies: 4)

  2. Angle solving (Replies: 5)