Question 1035742
<pre><font size=8><b>
(A)                 (B)
{{{drawing(400,400,-4.1,4.1,-4.1,4.1,grid(1),
graph(400,400,-4.1,4.1,-4.1,4.1,4sin((pi/4)x)) )}}}      {{{drawing(400,400,-4.1,4.1,-4.1,4.1,grid(1),
graph(400,400,-4.1,4.1,-4.1,4.1,4sin((pi/2)x)) )}}}</font></b>

The period of a function is the number of units along the x-axis
that span one complete cycle of the graph, where one complete
cycle is either
{{{graph(50,50,10,18,6,14,-4sin(pi/4*(x-10))+10))}}} or {{{graph(50,50,10,18,6,14,4sin(pi/4*(x-10))+10))}}} or {{{graph(50,50,10,18,6,14,4cos(pi/4*(x-10))+10))}}} or {{{graph(50,50,10,18,6,14,-4cos(pi/4*(x-10))+10))}}}

As you see in the first graph (A), the cycle {{{graph(50,50,10,18,6,14,-4sin(pi/4*(x-10))+10))}}}begins at -4 on
the x-axis and the cycle doesn't end until +4 on the x axis.
From -4 to +4 on the x-axis is a span of (+4)-(-4) = +4+4 = 8
units, so the period of the (A) graph is 8.

On graph (B), there are two complete cycles like this {{{graph(50,50,10,18,6,14,4sin(pi/4*(x-10))+10))}}} 
over the same span on the x-axis. Therefore the number of units on the 
x-axis that is spanned by just one cycle {{{graph(50,50,10,18,6,14,4sin(pi/4*(x-10))+10))}}} is 4.
So the period of the (B) graph is 4.

Edwin</pre>