If I am asked to find all solutions to 3 decimals of a trig function, and I know how to get each functions period, how to I get a common period so that I have the distance?
Thanks
For instance if I had:
$\displaystyle 2sin(3x)$=$\displaystyle cos(x)$
I know that $\displaystyle 2sin(3x)$ has a period of $\displaystyle \frac{2\pi}{3}$
and that $\displaystyle cos(x)$ has a period of just $\displaystyle 2\pi$
but when I writing it in terms of what I get from graphing it on my calc and then putting at the end $\displaystyle k\pi$ what would be the average or how could I find the $\displaystyle k\pi$?
I want to know how to do this for future reference...simply solving the equation won't help
Thanks so Much!!!
I see what you're up to. In this case both of the functions (sin(3x) and cos(x)) are periodic on $\displaystyle [0, 2 \pi)$ so any solutions will also have a period of $\displaystyle 2 \pi$. (See the graph below.)
If you have something like
$\displaystyle 2 sin(x/2) = cos(x)$
then we have to note that both functions are periodic on $\displaystyle [0, 4 \pi)$ so the solutions will have a period of $\displaystyle 4 \pi$.
-Dan