Cosecant Function Exploration

Explore the cosecant function, its graph, properties, and applications in trigonometry for Grade 11 students.

Grade 11 Math TrigonometryCosecant Function

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Includes

Fill in the BlanksMultiple Choice2 Short AnswerCustomTrue / False

Standards

CCSS.MATH.CONTENT.HSF.TF.B.5CCSS.MATH.CONTENT.HSF.TF.C.8

Topics

TrigonometryCosecantFunctionsGraphsGrade 11

8 sections · Free to use · Printable

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Read each question carefully and answer to the best of your ability. Show all your work where applicable.

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

2. The domain of csc(θ) excludes all values of θ where sin(θ) = .

3. The range of the cosecant function is or .

4. Which of the following is true about the asymptotes of y = csc(x)?

Asymptotes occur at x = nπ, where n is an integer.

Asymptotes occur at x = π/2 + nπ, where n is an integer.

There are no vertical asymptotes for the cosecant function.

Asymptotes occur at x = nπ/2, where n is an integer.

5. The period of the cosecant function is:

2π

π/2

Undefined

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

7. Sketch one period of the graph of y = 2csc(x). Label the asymptotes and any local maxima/minima.

8. The cosecant function is an odd function.

True

False

9. If sin(θ) = 1/2, then csc(θ) = 2.

True

False

10. Given that cos(θ) = 3/5 and θ is in Quadrant IV, find the value of csc(θ).