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Need help with determing domains of sin, cos, and tan

  1. Jun 20, 2011 #1
    1. The problem statement, all variables and given/known data

    Ok, this is not really a problem, but I need help on understanding the basics of sin, cos, tan, and their inverses.

    i was looking at http://www.analyzemath.com/DomainRange/domain_range_functions.html and it was saying that the domain for sin and cos is (-inf , + inf)
    and then for tan it is All real numbers
    except pi/1 + n*Pi
    but then for csc, it is All real numbers
    except n*Pi

    Can you explain why? I think I'm having trouble with figuring out how to find domains and I want to understand this before I start calculus. Please explain.
  2. jcsd
  3. Jun 20, 2011 #2


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    You might want to check the expression for x where tan x goes to +inf or -inf.
  4. Jun 20, 2011 #3
    You need to try a little yourself before asking, but I'll aid you this once..

    Tan(x) = Sin(x)/Cos(x)

    csc(x) = 1/Sin(x)

    What's the rule for dividing?
  5. Jun 20, 2011 #4


    Staff: Mentor

    I don't know what to make of "pi/1 + n*Pi ". The domain for the tangent function is all real numbers x, such that x ≠ (2n + 1)∏/2, where n is an integer. IOW, all reals except odd multiples of ∏/2.
  6. Jun 20, 2011 #5


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    Correction: this should be
    [tex]\frac{\pi}{2} + n\pi[/tex]
    . And you have to specify what n can equal, as Mark44 said.
  7. Jun 21, 2011 #6
    Hi Name_Ask,

    I'd like you to go to http://www.touchtrigonometry.org/" and play around with it a little bit.

    While you're there, make sure to do the following:

    • Look at the bottom left of the screen where you see the tig. function names and a value beside each.
    • Turn them all off by clicking on them.
    • Turn one on at a time.
    • Take notice of how often its pattern repeats, and when it starts.
    • Examine all the "x" values it can hold and the ones that are impossible.
    • Why are some of these Tig values impossible?
    • Click the active graph at any time to "Pause" your mouse, and look at what the line does on the Trig Circle to the left.
    • Compare what you see with your knowledge of what happens when a number is divided by 0.
    • Repeat with a new trig function.
    Last edited by a moderator: Apr 26, 2017
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