Understanding the Cosecant Function

This lesson explains how to graph the cosecant function over a specified interval. It highlights the relationship between the sine and cosecant functions, emphasizing that the cosecant is the reciprocal of the sine. The video demonstrates graphing the function using decimals.com, noting vertical asymptotes where the sine function equals zero. It also discusses the lack of amplitude in the cosecant graph and how to find additional points using the reciprocal relationship. The lesson concludes with a detailed analysis of the graph's concavity and additional points.

What is the relationship between the cosecant and sine functions?

• Cosecant is the square of sine.

• Cosecant is the reciprocal of sine.

• Cosecant is the derivative of sine.

• Cosecant is the integral of sine.

Why does the graph of the cosecant function have vertical asymptotes?

• Because sine function values are zero at those points.

• Because cosecant function values are one at those points.

• Because cosecant function values are zero at those points.

• Because sine function values are one at those points.

What is the period of the cosecant function?

• 180 degrees

• 360 degrees

• 90 degrees

• 720 degrees

Why does the cosecant function not have an amplitude?

• Because it is a constant function.

• Because it has a maximum value.

• Because it is a linear function.

• Because it extends indefinitely.

Where does the graph of the cosecant function have vertical asymptotes?

• At x = 90 degrees

• At x = 270 degrees

• At x = 45 degrees

• At x = 0, 180, 360 degrees

What happens to the cosecant function when the sine function equals one?

• Cosecant equals zero.

• Cosecant equals negative one.

• Cosecant equals one.

• Cosecant equals infinity.

What is the cosecant value when the sine of an angle is negative one?

• Infinity

• Negative one

• One

• Zero

How can additional points on the cosecant graph be found?

• By using the derivative of sine.

• By using the square of sine values.

• By using the integral of sine.

• By using the reciprocal of sine values.

What is the cosecant value when the sine of 30 degrees is 0.5?

• 0.5

• Infinity

• 1

• 2

What is the relationship between the concavity of sine and cosecant functions?

• They have the same concavity.

• They are both concave down.

• They are both concave up.

• They have opposite concavity.