# 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.

**Q5: **

Find the period of the function .

- A
- B
- C
- D

**Q6: **

What is the period 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 ?