Question

When do asymptotes happen in secant and cosecant?

a) At zeros of the function
b) At points of discontinuity
c) At critical points
d) At vertical lines

Answer 1

Asymptotes in secant and cosecant functions occur at points of discontinuity, where the sine and cosine functions are zero, resulting in division by zero which is undefined.

Step-by-step explanation:

Asymptotes in secant (sec) and cosecant (csc) functions occur at points where the cosine and sine functions, respectively, are zero because division by zero is undefined. For the secant function, which is the reciprocal of the cosine function, this happens at odd multiples of pi/2, or (2n+1)pi/2, where n is an integer.

Similarly, for the cosecant function, which is the reciprocal of the sine function, asymptotes occur at integer multiples of pi, npi, where n is an integer. So the correct answer to the question when do asymptotes happen in secant and cosecant functions is b) At points of discontinuity.