Find the Asymptotes f(x)=5csc(x)

Problem

ƒ(x)=5*csc(x)

Solution

1. Rewrite the function using the reciprocal identity for the cosecant function.

ƒ(x)=5/sin(x)

2. Identify the vertical asymptotes by finding where the denominator is equal to zero and the numerator is non-zero.

sin(x)=0

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

x=n*π

where *n* is any integer.

4. Determine the horizontal asymptotes by evaluating the limits as x approaches infinity. Since the cosecant function is periodic and oscillates between values, the limit does not exist.

No horizontal asymptotes.

Final Answer

Vertical Asymptotes: *x=n*π* for any integer *n

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