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Thread: A trigonometry question

  1. #1
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    A trigonometry question

    Hello,
    I am doing a trigonometric derivative problem, but I think I have forgotten the right step of when to add a $\displaystyle \pi n$ or when to add a 2$\displaystyle \pi n$. For example in my book, one of the problem says cosx = $\displaystyle
    \frac{{ - 1}}{2}
    $ $\displaystyle
    \Rightarrow
    $ x = $\displaystyle
    2\frac{\pi }{3} + 2\pi n
    $ or $\displaystyle
    4\frac{\pi }{3} + 2\pi n
    $. Now at other problem I see it says tanx = 1 $\displaystyle
    \Rightarrow
    $ x = $\displaystyle
    \frac{\pi }{4} + \pi n
    $ (n is an integer). Can you give me an explanation? Thank you for the help.
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  2. #2
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    Quote Originally Posted by Mathlv View Post
    Hello,
    I am doing a trigonometric derivative problem, but I think I have forgotten the right step of when to add a $\displaystyle \pi n$ or when to add a 2$\displaystyle \pi n$. For example in my book, one of the problem says Cosx = $\displaystyle
    \frac{{ - 1}}{2}
    $ $\displaystyle
    \Rightarrow
    $ x = $\displaystyle
    2\frac{\pi }{3} + 2\pi n
    $ or $\displaystyle
    4\frac{\pi }{3} + 2\pi n
    $. Now at other problem I see it says tanx = 1 $\displaystyle
    \Rightarrow
    $ x = $\displaystyle
    \frac{\pi }{4} + \pi n
    $ (n is an integer). Thank you for the help.
    The period of the sine and cosine functions is $\displaystyle 2\pi$. So you would find all solutions from the unit circle then add $\displaystyle 2\pi n$.

    The period of the tangent function is $\displaystyle \pi$. So you would find a solution then add $\displaystyle \pi n$.
    Last edited by Prove It; Feb 13th 2010 at 06:43 PM.
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  3. #3
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    Quote Originally Posted by Mathlv View Post
    Hello,
    I am doing a trigonometric derivative problem, but I think I have forgotten the right step of when to add a $\displaystyle \pi n$ or when to add a 2$\displaystyle \pi n$. For example in my book, one of the problem says cosx = $\displaystyle
    \frac{{ - 1}}{2}
    $ $\displaystyle
    \Rightarrow
    $ x = $\displaystyle
    2\frac{\pi }{3} + 2\pi n
    $ or $\displaystyle
    4\frac{\pi }{3} + 2\pi n
    $. Now at other problem I see it says tanx = 1 $\displaystyle
    \Rightarrow
    $ x = $\displaystyle
    \frac{\pi }{4} + \pi n
    $ (n is an integer). Can you give me an explanation? Thank you for the help.

    linking trig functions with the unit circle is the best way to get a feel for them in the early going. they are defined by the ratio of the sides one can inscribe therein, where the sides are those of a right triangle. if you study the geometry for a little while, it'll be like riding a bike thereafter.
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  4. #4
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    A trigonometric question

    Thank you very much for the response and the help Prove It and Vince. I get it now.
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