Vertical asymtotes of cotx and cscx?

Question

What are the vertical asymtotes of cotx and csc x. I know cofx is 1/tanx and cscx is 1/sinx. But how do i find the asymtotes? My other question is what are the limits for both of these for x=0 and x=pi

Answer 1

cotx = cosx / sinx

 

Set    sinx=0     and solve for x.

 

 

For cscx , set   sinx=0        and solve for x.

 

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To find the limits, you should use L'Hospital Rule.  That is when you take the derivative of the numerator over the derivative of the denominator.  You keep applying this rule until you have no indeterminate.

Answer 2

Cot(x)=cos(x)/sin(x)

 

for vertical asyptotes

 

Sin(x)=0

 

For a general solution to above

 

x=n*pi.         n=0,+1,+2,---------

                            -1,-2----------

 

Similarly cosec(x)=1/sin(x)

 

for vertical asyptotes  sin(x)=0

 

Solution is the same as above.