Understanding the Cosecant Function

This lesson explains how to graph the cosecant function over the interval from -2π to 2π. It highlights the relationship between the cosecant and sine functions, noting that the cosecant is the reciprocal of sine. The video demonstrates graphing the cosecant function using Desmos, identifying vertical asymptotes where the sine function is zero. It also shows how to find additional points on the cosecant graph by using the reciprocal relationship with sine values. The lesson emphasizes understanding the graph's behavior, such as its period and lack of amplitude, and the concavity relationship between sine and cosecant.

What is the relationship between the cosecant function and the sine function?

• Cosecant is the integral of sine.

• Cosecant is the derivative of sine.

• Cosecant is the square of sine.

• Cosecant is the reciprocal of sine.

Where is the cosecant function undefined?

• Where sine is equal to two.

• Where sine is equal to negative one.

• Where sine is equal to one.

• Where sine is equal to zero.

What is the period of the cosecant function?

• Three pi radians

• Two pi radians

• Four pi radians

• Pi radians

Why does the cosecant function not have an amplitude?

• Because it increases and decreases indefinitely.

• Because it is a constant function.

• Because it oscillates between fixed values.

• Because it is a linear function.

Where does the cosecant function have vertical asymptotes?

• At x equals three pi over two.

• At x equals pi over two.

• At x equals zero and multiples of pi.

• At x equals pi over four.

What happens to the cosecant function at points where the sine function equals one?

• Cosecant equals zero.

• Cosecant is undefined.

• Cosecant equals one.

• Cosecant equals negative one.

How does the concavity of the sine function relate to the cosecant function?

• They are both concave up at the same time.

• When sine is concave down, cosecant is concave down.

• They are both concave down at the same time.

• When sine is concave up, cosecant is concave down.

What is the cosecant value at x equals pi over six?

• One half

• Two

• One

• Zero

How can additional points on the cosecant graph be found?

• By using the reciprocal values of the sine function.

• By using the integral of the sine function.

• By using the square of the sine function.

• By using the derivative of the sine function.

What is the cosecant value at x equals five pi divided by six?

• Zero

• One

• Negative two

• Two