# Lesson Worksheet: The Graphs of Reciprocal Trigonometric Functions Mathematics • 10th Grade

In this worksheet, we will practice graphing cosecant, secant, and cotangent functions by understanding that they are related to the graphs of the sine, cosine, and tangent functions.

Q1:

Identify the graph of .

• A • B • C • D • E Q2:

Identify the graph of .

• A • B • C • D • E Q3:

Use the given graph of to determine the domain and range of the cosecant function in degrees. • BDomain: , range: or
• CDomain: , range: or
• DDomain: , range: or
• EDomain: , range:

Q4:

Using the given graph of , determine the domain and range of the cotangent function in radians. • ADomain: , , , range:
• BDomain: , , , range:
• CDomain: , range: , ,
• DDomain: , , , range:
• EDomain: , , , range:

Q5:

Find the -intercept and the -intercept of the graph of for .

• AThere is no -intercept and .
• B and there is no -intercept.
• CThere is no -intercept and there is no -intercept.
• D and there is no -intercept.
• EThere is no -intercept and .

Find the coordinates of the local maxima and minima of the graph of for .

• AMinimum: , maximum:
• BMaximum: , minimum:
• CMaximum: , minimum:
• DMaximum: , minimum:
• EMaximum: , minimum:

Identify which of the following is the graph of for .

• A • B • C • D • E Q6:

Find the -intercept and the -intercept of the graph of for .

• A, and there is no -intercept.
• BThere is no -intercept, and there is no -intercept.
• CThere is no -intercept, and .
• D, and there is no -intercept.
• EThere is no -intercept, and .

Find the coordinates of the local maxima and minima of the graph of for .

• AMaximum: , minimum:
• BMaximum: , minimum:
• CMaximum: , minimum:
• DMaximum: , minimum:
• EMaximum: , minimum:

Identify which of the following is the graph of for .

• A • B • C • D • E Q7:

By sketching the graphs and on the same axes, find the number of solutions of the equation for .

Q8:

By sketching the graphs of , , and , determine which two of the three functions are equal.

• A
• B
• C
• D

Q9:

• A
• B
• C
• D
• E

Q10:

• A
• B
• C
• D
• E