What is the Domain Range and Vertical Asymptote of Cosecant

The video tutorial explains how to find the domain and range of the cosecant function. It begins by graphing the sine function, as cosecant is its reciprocal. The tutorial highlights the creation of vertical asymptotes at the intercepts of the sine function, which are points where the cosecant function is undefined. The domain is all real numbers except where x equals multiples of π. The range is from negative infinity to -1 and from 1 to infinity, as there are no output values between -1 and 1.

What is the first step in finding the domain and range of the cosecant function?

• Graph the parent function of sine

• Calculate the derivative of the function

• Graph the tangent function

• Find the zeros of the function

How are vertical asymptotes of the cosecant function determined?

• By the maximum points of the sine function

• By the slope of the sine function

• By the intercepts of the sine function

• By the minimum points of the sine function

What happens to the cosecant graph at the intercepts of the sine function?

• It reaches minimum values

• It reaches maximum values

• It forms vertical asymptotes

• It forms horizontal asymptotes

Which of the following is excluded from the domain of the cosecant function?

• Values between -1 and 1

• Negative numbers

• Multiples of π

• All real numbers

What is the range of the cosecant function?

• From negative infinity to -1 and from 1 to infinity

• Only positive numbers

• All real numbers

• Between -1 and 1