Cosecant Function Exploration

A Grade 10 math worksheet exploring the cosecant function, its definition, graph, period, and relationship to the sine function.

Grade 10 Math TrigonometryCosecant Function

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Includes

Fill in the BlanksMultiple Choice2 Short AnswerCustomTrue / False

Standards

CCSS.MATH.CONTENT.HSF.TF.A.2CCSS.MATH.CONTENT.HSF.TF.B.5

Topics

cosecanttrigonometryfunctionsgraphingperiod

8 sections · Free to use · Printable

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Cosecant Function Exploration

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Read each question carefully and answer to the best of your ability. Show all your work for full credit.

1. The cosecant function, denoted as csc(θ), is the reciprocal of the function.

2. Therefore, csc(θ) = 1 / .

3. The cosecant function is undefined when the function is equal to zero.

4. What is the period of the cosecant function?

2π

π/2

Depends on the amplitude

5. At what angles (in radians) is csc(θ) undefined?

π/2 + nπ

nπ

2nπ

π/4 + nπ

6. Describe the relationship between the graph of y = sin(x) and the graph of y = csc(x). How can you use the sine graph to help sketch the cosecant graph?

7. Evaluate the following exactly:

a) csc(π/2) =

b) csc(π) =

c) csc(3π/2) =

d) csc(2π) =

8. The range of the cosecant function is (-∞, -1] U [1, ∞).

True

False

9. The graph of y = csc(x) has vertical asymptotes at x = π/2 + nπ, where n is an integer.

True

False

10. If sin(θ) = 0.5, what is the value of csc(θ)?