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Math Help - 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 \pi n or when to add a 2 \pi n. For example in my book, one of the problem says cosx = <br />
\frac{{ - 1}}{2}<br />
<br />
 \Rightarrow <br />
x = <br />
2\frac{\pi }{3} + 2\pi n<br />
or <br />
4\frac{\pi }{3} + 2\pi n<br />
. Now at other problem I see it says tanx = 1 <br />
 \Rightarrow <br />
x = <br />
\frac{\pi }{4} + \pi n<br />
(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 \pi n or when to add a 2 \pi n. For example in my book, one of the problem says Cosx = <br />
\frac{{ - 1}}{2}<br />
<br />
 \Rightarrow <br />
x = <br />
2\frac{\pi }{3} + 2\pi n<br />
or <br />
4\frac{\pi }{3} + 2\pi n<br />
. Now at other problem I see it says tanx = 1 <br />
 \Rightarrow <br />
x = <br />
\frac{\pi }{4} + \pi n<br />
(n is an integer). Thank you for the help.
    The period of the sine and cosine functions is 2\pi. So you would find all solutions from the unit circle then add 2\pi n.

    The period of the tangent function is \pi. So you would find a solution then add \pi n.
    Last edited by Prove It; February 13th 2010 at 06:43 PM.
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  3. #3
    Member
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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 \pi n or when to add a 2 \pi n. For example in my book, one of the problem says cosx = <br />
\frac{{ - 1}}{2}<br />
<br />
\Rightarrow <br />
x = <br />
2\frac{\pi }{3} + 2\pi n<br />
or <br />
4\frac{\pi }{3} + 2\pi n<br />
. Now at other problem I see it says tanx = 1 <br />
\Rightarrow <br />
x = <br />
\frac{\pi }{4} + \pi n<br />
(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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    Joined
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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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