Which of the following is an asymptote of y = csc (x) ? x = - pi x=-pi/3 x=pi/4 x = pi/2

Question

Sariah Hammond

Mathematics

30 May, 23:25

Which of the following is an asymptote of y = csc (x) ? x = - pi x=-pi/3 x=pi/4 x = pi/2

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Answers (1)

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Shyann Arellano · Answer 1

x = - π

Step-by-step explanation:

The asymptote occur when the y value does not exist. We know that the y value doesnt exist when the denominator of a function equals zero.

csc (x) can be written as 1/sin (x)

So to find the asymptote we just need to know where sin (x) = 0, because it is illegal to divide by zero.

sin (x) = 0 at 0, π, 2π, and so on

So an asymptote of the function would be pi times any whole number. x=-π is the only answer that multiplied π by a whole number, so it is the only asymptote.