limits,graphing

Question

I really need help understanding how to graph these. I freal out when I see anything with trig words and get really confused. So the question is asking :

Write all the vertical asymptotes of cotx and cscx. Study the sided limits at x=0 and x=pi and use the results to sketch a graph of the two functions.

How do i go about doing this ? I would really appreciate a detailed explanation :)

Answer 1

This is easy. Learn from this answer, and learn better from your class lectures and book.

 

Consider cot x, defined as the quotient of cos x and sin x. So there's a denominator; when would it ever be zero?

 

Answer: The sine function has zeros at x = every multiple of pi: 0, pi, 2pi, 3pi, etc.--as well as the negative versions of this list.

 

For consideration of csc x, which is the reciprocal of sine, the answer would be the same as above.

 

You can confirm some of this by a graphing calculator (in radian mode) with window set at, say x from - 2pi to 2 pi, and y range from (say) -10 to 10.

 

You can use the internet--Google whatever you want, such as "graph of cosecant function"

 

Bottom line: vertical asymptotes come about from zeros of denominators