Find the Asymptotes y=csc(x)

Problem

y=csc(x)

Solution

1. Identify the function as the reciprocal of the sine function.

y=1/sin(x)

2. Determine the condition for vertical asymptotes by finding where the denominator is equal to zero.

sin(x)=0

3. Solve the equation for x to find the locations of the vertical asymptotes.

x=n*π

where *n* is any integer.

4. Analyze the behavior of the function for horizontal asymptotes. Since the range of sin(x) is [−1,1] the range of csc(x) is (−∞,−1]∪[1,∞)

(lim_x→∞)(csc(x))=does not exist

Final Answer

Vertical Asymptotes: *x=n*π, Horizontal Asymptotes: None

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