# Worksheet: Amplitude and Period of Trigonometric Functions

In this worksheet, we will practice finding the amplitude and the period of sine, cosine, and tangent functions.

Q1:

Determine the amplitude and the period of the shown function.

• Aamplitude , period
• Bamplitude , period
• Camplitude , period
• Damplitude , period
• Eamplitude , period

Q2:

What is the period of ?

• A
• B
• C
• D
• E

Q3:

What is the period of ?

• A
• B
• C
• D
• E

Q4:

What is the period of ?

• A
• B
• C
• D
• E

Q5:

Find the period of the function .

• A
• B
• C
• D

Q6:

What is the period of the function ?

• A
• B
• C
• D
• E

Q7:

What is the period of ?

• A
• B
• C
• D
• E

Q8:

What is the amplitude of the function ?

• A
• B
• C
• D
• E

Q9:

Simplify .

• A
• B
• C
• D

Q10:

What is the amplitude of the function ?

• A
• B
• C
• D
• E

Q11:

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

• A
• B
• C
• D

Q12:

What is the maximum value of the function ?

• A
• B
• C
• D
• E

Q13:

Let . What is the smallest positive value of for which holds?

• A
• B
• C
• D
• E

Q14:

Since for every number , we can conclude that .

• AThe period of the sine function is a divisor of .
• BThe period of the sine function is .
• CThe period of the function is 1.
• DThe period of the sine function is .
• ESine is an even function.

Q15:

What is the period of the function ?

• A
• B
• C
• D
• E

Q16:

What is the amplitude of ?

• A14
• B5
• C12
• D
• E

Q17:

has period and has period . What is the period of their sum ?

• A
• B
• C
• D and
• E

Q18:

Consider the function .

Determine the amplitude.

• Aamplitude
• Bamplitude
• Camplitude
• Damplitude
• Eamplitude

Determine the period.

• Aperiod
• Bperiod
• Cperiod
• Dperiod
• Eperiod

Q19:

What is the period of the function ?

• A
• B
• C
• D
• E

Q20:

What is the period of the function ?

• A
• B
• C
• D
• E

Q21:

What is the amplitude of the function ?

Q22:

What is the amplitude of ?

Q23:

What is the frequency of the function ?

• A
• B
• C
• D
• E

Q24:

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?

• Aone and a half seconds later
• Bone-third of a second later
• Cone second later
• Dhalf a second later
• Etwo seconds 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

Q25:

What is the maximum value of ?