Understanding the Cosecant Function

This video tutorial explains how to graph the cosecant function using the reciprocal identity, where cosecant is the reciprocal of sine. It covers determining sine function values, calculating their reciprocals, and plotting these to form the graph of the cosecant function. The tutorial also discusses vertical asymptotes that occur when sine is zero and demonstrates how to graph cosecant for both positive and negative sine values.

What is the reciprocal identity used to graph the cosecant function?

• Cosecant = 1 divided by cotangent

• Cosecant = 1 divided by sine

• Cosecant = 1 divided by tangent

• Cosecant = 1 divided by cosine

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CCSS.HSF.TF.A.2

If sine data is equal to 1, what is the value of cosecant data?

• 0

• 1

• -1

• Undefined

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CCSS.HSF.TF.A.2

What happens to the cosecant function when sine data is zero?

• Cosecant is zero

• Cosecant is undefined

• Cosecant is one

• Cosecant is negative

Where do vertical asymptotes occur in the graph of the cosecant function?

• Where sine data is 1/2

• Where sine data is 0

• Where sine data is 1

• Where sine data is -1

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CCSS.HSF.TF.A.2

What is the cosecant value when sine data is 1/2?

• 4

• 1

• 2

• 1/2

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CCSS.HSF.TF.A.4

As sine data approaches zero, what happens to the cosecant value?

• It increases

• It decreases

• It becomes undefined

• It approaches zero

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CCSS.HSF.TF.A.2

What is the cosecant value when sine data is -1/2?

• -4

• -1/2

• -2

• -1

How does the graph of the cosecant function behave when sine data is negative?

• It mirrors the positive sine values

• It becomes undefined

• It remains positive

• It becomes zero

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CCSS.HSF.TF.A.2

What is the cosecant value when sine data is -1/4?

• -1/4

• -1

• -2

• -4

What is a key method to remember when sketching the graph of the cosecant function?

• Use the reciprocal identity

• Use the cosine identity

• Use the tangent identity

• Use the cotangent identity