The other tutor's answer is correct about the period, but
incorrect about the vertical asymptotes.
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The period of 



is 

and has vertical asymptotes wherever 
bx is an odd multiple of 

Therefore the period of



is 

and has vertical asymptotes wherever 
2x is an odd multiple of 

Odd numbers are represented by 2n-1, so 
between -p and +p,





Multiplying through by 4



Dividing all three sides by p



Adding 1 to all three sides:



Dividing all three sides by 2



And since n is an integer, n=-1,0,1,2

So when n=-1, (2n-1)pi/2 = -3p/4
And when n=1, (2n-1)pi/2 = -p/4
And when n=1, (2n-1)pi/2 = p/4
And when n=1, (2n-1)pi/2 = 3p/4

So in the interval (-p,p),
the graph continues through 4 periods, and there are 4 vertical 
asymptotes at: 

x = -3p/4, approximately -2.4
x = -p/4, approximately -0.8
x = p/4, approximately 0.8
x = 3p/4, approximately 2.4

the 4 green lines are the 4 vertical asymptotes:



Edwin