Free Printable Trig phase shifts

1.

What is the phase shift for y = 4cos(¹/₂x +π) - 2?

a)

left pi/2

b)

right pi/2

c)

right 2pi

d)

left pi

2.

5. Write an equation for the cosine function with amplitude 3, period 2pi, phase shift of pi, and vertical shift of 5.

a)

y = 5cos(x - pi) + 3

b)

y = 3cos(x - pi) + 5

c)

y = 3cos(2x - pi) + 5

d)

y = 5cos(2x - pi) + 3

3.

8. What is the period for y = 4cos(¹/₂x +π) - 2?

a)

pi/2

b)

pi

c)

3pi

d)

4pi

4.

What is the phase shift for the function

f(x) = -2sin(4x + π) - 1

a)

π right

b)

4π

c)

2π

d)

π left

5.

What is the vertical shift for

y = 4 cos(x +π) - 2?

a)

up 2

b)

left 2

c)

right 2

d)

down 2

6.

In the functions f(x)=Asin(Bx + C) + D, D represents what?

a)

Amplitude

b)

Midline

c)

Phase Shift

d)

Vertical Translation

e)

Horizontal Translation

7.

In the equation $y\ =\ \frac{1}{3}\cos\left(\frac{1}{2}x+\frac{\pi}{3}\right)$ , what is the phase shift?

a)

$\frac{\pi}{3}$

b)

$\frac{2\pi}{3}$

c)

$\pi$

d)

$\pi$

8.

What is the phase shift of the curve $y=10\sin\left(2x-20\right)+25$ ?

a)

-20

b)

20

c)

10

d)

-10

9.

Which is an equation of the cosine function with a period of $\pi$ & a phase shift of right $\frac{\pi}{2}$ ?

a)

$y=2\cos\left(\frac{x}{2}-\frac{\pi}{4}\right)$

b)

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

c)

$y=2\cos\left(x-\frac{\pi}{2}\right)$

d)

$y=2\cos\left(2x-\frac{\pi}{2}\right)$

10.

What is the phase shift for $y=4\cos\left(\frac{1}{2}x+\pi\right)-2$

a)

left $\frac{\pi}{2}$

b)

right $\frac{\pi}{2}$

c)

right $2\pi$

d)

left $\pi$

11.

Determine the period of $y=\sin\left(\pi\theta\right)+3$

a)

$2\pi$

b)

2

c)

$\pi$

d)

$2\pi^2$

12.

Write an equation for a cosine function with amplitude 3, period $2\pi$ , phase shift of $\pi$ , and vertical shift of 5.

a)

$y=5\cos\left(x-\pi\right)+3$

b)

$y=3\cos\left(x-\pi\right)+5$

c)

$y=3\cos\left(2x-\pi\right)+5$

d)

$y=5\cos\left(2x-\pi\right)+3$

13.

What is the period for $y=4\sin\left(\frac{1}{2}x+\pi\right)+2$

a)

$\frac{\pi}{2}$

b)

$\pi$

c)

$3\pi$

d)

$4\pi$

14.

What is the phase shift for the function $f\left(x\right)=-2\sin\left(4\theta+\pi\right)-1$ ?

a)

$\pi$ right

b)

$-\pi$

c)

$\frac{\pi}{4}$

d)

$\pi$ left

e)

$-4\pi$

15.

What is the vertical shift for $y=4\cos\left(x+\pi\right)-2$ ?

a)

up 2

b)

left 2

c)

right 2

d)

down 2

16.

In the equation $y\ =\ \frac{1}{3}\cos\left(\frac{1}{2}x+\frac{\pi}{3}\right)$ , what is the phase shift?

a)

$-\frac{2\pi}{3}$

b)

$\frac{2\pi}{3}$

c)

$\frac{\pi}{3}$

d)

$-\frac{\pi}{3}$

17.

Find the phase shift of $f\left(x\right)=6\sin\left(3\theta-3\pi\right)$

a)

Right $3\pi$

b)

Left $3\pi$

c)

Right $\pi$

d)

Left $\pi$

18.

Where is the midline for
y=2cos(1/3x +π/6) +2

a)

1/3

b)

-2

c)

+2

d)

4

19.

Describe the horizontal shift.

a)

left 3π / 4

b)

left 4π / 3

c)

right 3π

d)

right 3π / 4

20.

6. What is the vertical shift for y = 4cos(¹/₂x +π) - 2?

a)

up 2

b)

left 2

c)

right 2

d)

down 2

21.

Which value helps identify a horizontal shift in the following function y=a*sin(bx-c)+d?

a)

a

b)

b

c)

c

d)

d

22.

Which value helps identify the period in the following function y=a*sin(bx-c)+d?

a)

a

b)

b

c)

c

d)

d

23.

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

a)

π/3

b)

π/6

c)

2π/3

d)

2π/6

24.

What is the phase shift?
y=-2sin(x-π)

a)

π left

b)

π right

c)

none

d)

2π right

25.

Which function below describes only the following transformations?
Left π/2
Period: π

a)

csc2(x+π/2)

b)

2sec(x+π/2)

c)

tanπ/2(x+2)

d)

2-csc(x+π/2)

26.

What is the amplitude of Y=4sinx -2

a)

2

b)

4

c)

-2

d)

-4

Trig phase shifts

Total questions: 26

Worksheet time: 2hrs 10mins

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