Can someone please help me find 2 asymptotes and the period for the equation y=csc(pi*x)/(4)? I tried working out the period and got 8/x but that doesn't seem right, did I do something wrong?

Question

anonymous · Answer

I also have the graph if that helps, I just keep getting confused!

anonymous · Answer

by looking at the graph would my two asymptotes be 4 and 7 or am i wrong?

anonymous · Answer

attachment

anonymous · Answer

i need to know how to find the answer though :/

amistre64 · Answer

csc is the reciprocal of sin, and has a normal period of 2pi  right?

when does the argument used in the function equal 2pi?

amistre64 · Answer

for example,  spose they said csc(4x)

4x = 2pi  when  x = 2pi/4   so the period becomes pi/2

anonymous · Answer

so then you just continue to divide by pi/2 or would it be +- pi/2?

anonymous · Answer

oh that was for the period? i was thinking asymptotes, sorry!

amistre64 · Answer

the period is a measure of distance between start to finish, so we would just say pi/2

amistre64 · Answer

your problem here i think states:

csc(x*pi/4)

x*pi/4 = 2pi,  solving for x we get x=8 for the period

anonymous · Answer

would i be able to create a formula to find the asymptotes by using the period?

amistre64 · Answer

not 8/x

amistre64 · Answer

im sure you could ... sin is related to csc, so shen sin =0 we have a divide by zero error which creates the asymptote

anonymous · Answer

this is the problem: $$y=\csc \frac{\pi*x}{4}$$

amistre64 · Answer

when does sin(x*pi/4) = 0?

amistre64 · Answer

sin is equal to 0 at its period ends, and at the midpoint of the period

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