what is the period of the function y=1/2sin (x/3-pi)

Question

mathmale · Answer

We'd approach this problem in a fashion quite similar to (not the last problem, but the one before it).

mathmale · Answer

You can ignore the (1/2) and focus on the argument, (x/3 - pi) , of the sine function
Rewrite that x/3 as (1/3)*x.
Remember, I keep calling that coefficient of x    ' b '.

Remember our formula for the period?

Write it out, substituting the appropriate value for b.

anonymous · Answer

so to 2pi/b=x/3?

mathmale · Answer

Take another look, quickly.  What is the coefficient of x in your function?  Remember how I re-wrote x/3 as (1/3)x?

b = ?

anonymous · Answer

b=1/3?

mathmale · Answer

Right, so your period is 2Pi/b, or 2Pi/ ( ? )     =      ?

anonymous · Answer

2pi/1/3?

mathmale · Answer

I'd feel better if you were to write it as 2Pi/(1/3) (with parentheses).

Now please evaluate 2Pi/(1/3).

anonymous · Answer

gt the answer! :)) 6pi! but how did u no how to rewrite?

mathmale · Answer

Think about what x/3 means.$$x/3=\frac{ x }{ 3 }=\frac{ 1 }{ 3 }x$$so we see that the (constant) coefficient of x is (1/3).  OK with that?

mathmale · Answer

Once again:  You must be able to identify the coefficient of x (or of t).  Re-writing x/3 as (1/3)x makes it easier to recognize that b is (1/3) here.

anonymous · Answer

got it! ur awesome!

mathmale · Answer

thank you very much , lyubas.  that really makes me feel good.
I need to stop now, as I've been invited to visit a neighbor.  Remember, you can send me private messages at any time.  We could set up an appointment or two if need be.
But for now, good night, wishing you all the best!

anonymous · Answer

ok :( have fun

mathmale · Answer

:)