Write an expression for all of the vertical asymptotes of y=-3 csc(pi/4 *x)

Can you list step by step to show how to do it , I don't understand this problem !!! Thanks

1 answer

you know that sin(pi/4 x)=0 when pi/4 x is a multiple of pi.

That is, pi/4 x = k*pi
x = k*pi * 4/pi = 4k
So, when x is a multiple of 4, sin(pi/4 x) is zero. That is where csc(pi/4 x) has vertical asymptotes.