Free Printable Warm Up - Practice Sinusoidal Functions

1.

What is the amplitude of the graph?

a)

3

b)

2

c)

-3

d)

-2

2.

In the functions f(x)=Asin[B(x + C)] + D,

D represents what?

Check all that apply.

a)

Period

b)

Frequency

c)

Phase Shift

d)

Vertical Shift

e)

Midline

3.

Sine or Cosine?

a)

y=sinx

b)

y=cosx

4.

What is NOT a possible equation for the function?

a)

$y=-5\cos\left(x-\pi\right)$

b)

$y=-5\sin x$

c)

$y=5\sin\left(x+\frac{\pi}{2}\right)$

d)

$y=5\cos\left(x-8\pi\right)$

5.

What is the period of y = 2cos(3x)-5

a)

π/3 or 60 degrees

b)

6π or 1080 degrees

c)

2π/3 or 120 degrees

d)

3π or 540 degrees

6.

Find the equation of the midline of the graph shown.

a)

y = 1

b)

y = 2

c)

y = 3

d)

y = 0

7.

Atlanta's temperature in 2024 can be represented by the following function, where F(t) is measured in Fahrenheit and t is the days passed. What was the Atlanta's low?

$F\left(t\right)=-28\cos\left(\frac{2\pi}{365}\left(t\right)\right)+57$

a)

57 degres

b)

28 degrees

c)

75 degrees

d)

29 degrees

8.

Find the period of the graph shown.

a)

2

b)

4

c)

6

d)

8

9.

Which line is y=2sinx

a)

Black

b)

Blue

c)

Red

10.

At a pier, scientists measure the depth of the water according to the tides. At high tide, the water depth is 8 feet. At low tide, 6.2 hours later, the depth is 5 feet. Which of the following shows how you would fill-in the next 4 depths in the table?

a)

6.5, 5, 6.5, 8

b)

4, 0, 4, 8

c)

5, 2.5, 5, 8

d)

5, 8, 5, 8

11.

At a pier, scientists measure the depth of the water according to the tides. At high tide, the water depth is 8 feet. At low tide, 6.2 hours later, the depth is 5 feet. Use the equation or table to decide: how often does the tide cycle repeat?

a)

Once every 3.1 hours.

b)

Once every 6.2 hours.

c)

Once every 9.3 hours.

d)

Once every 12.4 hours.

12.

A complete cycle of the function $y=A\cos\left(Bx\right)+C$ is shown. What is the value of B?

a)

$\frac{\pi}{4}$

b)

$\frac{\pi}{8}$

c)

8

d)

$\frac{8\pi}{3}$

13.

What is the period of the function shown in the given graph?

a)

7

b)

8

c)

15

d)

16

14.

The average person’s blood pressure is modelled by the function f(t)=20sin(160πt)+100,

where f(t) represents the blood pressure at time t measured in minutes.

What is the blood pressure at t=0.07 minute?

a)

111.525

b)

88.244

c)

100

d)

120

15.

The average daily high temperature (in celcius) in Karachi, Pakistan, on the t-th day of the year is approximately modelled by
$T\left(t\right)=29-5\cos\left(\frac{2\pi\left(t-12\right)}{365}\right)$ .

Find the highest average daily highs in Karachi. Give exact answer.

a)

-5

b)

24

c)

29

d)

34

16.

What graph is shown here?

a)

b)

c)

d)

17.

Which is true?

a)

The blue graph is cos and the green graph is -cos.

b)

The blue graph is sin and the green graph is -sin.

c)

The blue graph is -cos and the green graph is cos.

d)

The blue graph is -sin and the green graph is sin.

18.

What is the range of the graph of: $y=5\sin\left(x\right)-4$

a)

$\left[-5,\ 5\right]$

b)

$\left[-9,\ 1\right]$

c)

$\left[1,\ 9\right]$

d)

$\left[-4,\ 4\right]$

19.

What would be the ideal (expected) period for this data?

a)

12 since there are 12 months in the year.

b)

365 since there are 365 days in the year.

c)

24 since there are 24 hours in a day.

d)

5 since May is the 5th month.

20.

The temperature in an office is controlled by an electronic thermostat. The temperatures vary according to the sinusoidal function:

y = 5 sin( π/12 (x – 11)) +18

where y is the temperature (ºC) and x is the time in hours past midnight. What are the minimum and maximum temperatures in the office?

a)

12ºC and 23ºC

b)

13ºC and 23ºC

c)

5ºC and 18ºC

d)

11ºC and 23ºC

21.

When you board a Ferris wheel your feet are 1 foot off the ground. At the highest point of the ride, your feet are 99 feet above the ground. It takes 30 seconds for the ride to complete one full revolution. Write a trigonometric equation for your height above the ground at t seconds after the ride starts. Find at what two times within one cycle you are exactly at 90 feet off the ground.

a)

14.3, 18.6

b)

12.1, 17.9

c)

13.4, 16.2

d)

10.5, 15.3

Warm Up - Practice Sinusoidal Functions

Total questions: 21

Worksheet time: 2hrs 2mins

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