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Periodicity of Inverse Trigonometric Functions

  1. Oct 28, 2008 #1
    1. The problem statement, all variables and given/known data

    My problem from before has been more or less resolved, but now I have a new, bigger problem. I need to figure out how to find recuring values for trig functions. I'm having a hard time figuring out how to

    1. Get the equations associated with a given value for the trig functions
    2. Actually finding all of those values.

    This is a problem for me because I can tell that this is a critical concept.

    2. Relevant equations

    My book gives me these equations for radians: x=30+360n or x=150+360n
    For radians: pi/6+2piN or 5pi/6+2piN. The book goes into little detail as to how to work these equations, and I would very much appreciate it if someone could tell me how to work them.

    3. The attempt at a solution

    One problem reads: List the solutions in degrees: cos^-1(1/2)= 60 (degrees), 300, 420, 660, 780, 1020, and I have absolutely no idea how they came up with that answer. Like I said before, I would really appreciate it if someone could help me with this, and please tell me if I should clarify any part of what I'm asking.
  2. jcsd
  3. Oct 28, 2008 #2


    Staff: Mentor

    Think about it the other way around: What are all the angle measures (in degrees) for which the cosine of that angle is 1/2?

    There are going to be two angles in each 360 degree full circle, so (in degrees),
    .5 = cos(60) = cos(300) = cos(360 + 60) = cos(360 + 300) = cos(720 + 60) = cos(720 + 300) = ...

    All of the cosine function arguments are of the form 60 + n*360 or 300 + n*360, where n is an integer. (I have shown them for nonnegative integers n, but the pattern applies also to negative integers.
  4. Oct 28, 2008 #3
    Whoa, that just clicked beautifully. THANK YOU! I'm pretty sure I understand what I'm doing now.
  5. Oct 29, 2008 #4


    Staff: Mentor

    You're welcome!
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