# Worksheet: Period of a Cyclic Function

Q1:

Let be a periodic function. If is the smallest nonzero value for which for all , what do we call ?

• Athe vertical shift of
• Bthe horizontal shift of
• Cthe period of
• Dthe amplitude of
• Ethe initial value of

Q2:

What is the definition of a periodic function for some nonzero constant ?

• A for all
• B for all
• C for all
• D for all
• E for all

Q3:

Which of the following relates the frequency and the period of a trigonometric function?

• A
• B
• C
• D
• E

Q4:

State if the following is true: If has period , then so . Therefore, also has a period .

• Afalse
• Btrue

Q5:

A function has a period . Among the following statements, which one is NOT necessarily true?

• A
• B
• C
• D

Q6:

A point is traveling on a unit circle at a speed of one complete rotation per second.

If its position represents an angle at a time , when will it have the same position again?

• Atwo seconds later
• Bone and a half seconds later
• Cone second later
• Dhalf a second later
• Eone-third of a second later

How would you express the angle representing its position at this time?

• A
• B
• C
• D
• E

Deduce what the period of the cosine and sine functions is.

• A
• B
• C
• D
• E

Q7:

Consider the function .

Determine the amplitude.

• Aamplitude
• Bamplitude
• Camplitude
• Damplitude
• Eamplitude

Determine the period.

• Aperiod
• Bperiod
• Cperiod
• Dperiod
• Eperiod

Q8:

The figure shows the graph of .

Which of the following is a graph of ?

• A
• B
• C
• D
• E

Q9:

Find the range and period of the function by drawing the function between 0 and .

• Arange, period
• Brange, period
• Crange, period
• Drange, period

Q10:

What is the period of the function ?

• A
• B
• C
• D
• E

Q11:

What is the period of the function ?

• A
• B
• C
• D
• E

Q12:

What is the period of the function ?

• A
• B
• C
• D
• E

Q13:

What is the period of the function ?

• A10
• B6
• C
• D5
• E

Q14:

What is the period of ?

• A
• B
• C
• D
• E

Q15:

What is the period of ?

• A
• B
• C
• D
• E

Q16:

Find the period of the function .

• A
• B
• C
• D

Q17:

What is the period of ?

• A
• B
• C
• D
• E