# A trigonometry question

• Feb 13th 2010, 06:11 PM
Mathlv
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.
• Feb 13th 2010, 06:14 PM
Prove It
Quote:

Originally Posted by Mathlv
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 $\displaystyle \pi n$.
• Feb 13th 2010, 06:36 PM
vince
Quote:

Originally Posted by Mathlv
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.
http://www.math.ucsd.edu/~jarmel/mat...cle_Angles.png
• Feb 13th 2010, 09:13 PM
Mathlv
A trigonometric question
Thank you very much for the response and the help Prove It and Vince. I get it now.