graphing: find asymptotes of y = 4 csc(1/2x - pi/4)

[messa]

Find the asymptotes for y = 4csc(1/2x - pi/4)

I have the period of 4 pi and this is my work

0 <= 1/2-pi/4 <= pi

pi/4 1/2x 5pi/4

pi/2 <= x <= 5pi/2

Would the asymptote be only pi/2?

 

[stapel]

Since trig functions are periodic, it is highly unlikely that something that should happen every period would happen only once ever ("only pi/2").

However, I'm afraid I don't follow your working. What is the meaning of your second line? And what are you trying to accomplish?

Please be specific. Thank you.

Eliz.

 

[messa]

I was solving for x by subtracting pi/4 and dividing by 1/2

 

[skeeter]

the cosecant function is undefined at all integer multiples of pi.

(1/2)x - pi/4 = k(pi) where k is an integer

x - pi/2 = 2k(pi)

x = 2k(pi) + pi/2 = pi(2k + 1/2) = pi[(4k+1)/2]

vertical asymptotes will occur at ...

x = {..., -11pi/2, -7pi/2, -3pi/2, pi/2, 5pi/2, 9pi/2, 13pi/2, ...}