# Common Period

• December 1st 2006, 11:05 AM
qbkr21
Common Period
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
• December 1st 2006, 11:15 AM
topsquark
Quote:

Originally Posted by qbkr21
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

Can I just take a moment to say:

Huh? :confused:

Perhaps you could post the actual problem?

-Dan
• December 1st 2006, 11:32 AM
qbkr21
Re:

$2sin(3x)$= $cos(x)$

I know that $2sin(3x)$ has a period of $\frac{2\pi}{3}$

and that $cos(x)$ has a period of just $2\pi$

but when I writing it in terms of what I get from graphing it on my calc and then putting at the end $k\pi$ what would be the average or how could I find the $k\pi$?

I want to know how to do this for future reference...simply solving the equation won't help

Thanks so Much!!!
• December 1st 2006, 11:57 AM
topsquark
Quote:

Originally Posted by qbkr21

$2sin(3x)$= $cos(x)$

I know that $2sin(3x)$ has a period of $\frac{2\pi}{3}$

and that $cos(x)$ has a period of just $2\pi$

but when I writing it in terms of what I get from graphing it on my calc and then putting at the end $k\pi$ what would be the average or how could I find the $k\pi$?

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 $[0, 2 \pi)$ so any solutions will also have a period of $2 \pi$. (See the graph below.)

If you have something like
$2 sin(x/2) = cos(x)$
then we have to note that both functions are periodic on $[0, 4 \pi)$ so the solutions will have a period of $4 \pi$.

-Dan