Given the equation, describe how the phase shift changed from the parent graph.

The graph shifted to the left by \frac{7\pi}{3}units.

13.7 Graphing Sine and Cosine Functions (translations)

Period, amplitude, & phase shift of trigonometric functions. #trigonometry #mathematics #translations Pre-Calc Chapter 4 and Functions & trig 13.7

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Questions 18

Answers

1
Write a sine function that has amplitude 4, Period 4π, phase shift - 2, and vertical shift +1
y = 4sin1/2(x+2)+1
y = -4sin1/2(x-2)+1
y = 4sin4π(x+2)+1
y = 4cos1/2(x+2)+1
2
Write the equation for the graph, using a -sin function.
-sin(x-π)+3
3sinx
-sinx-3
-3sin(x-π)
3
Which equation could match the graph shown?
y = 2 cos (x)
y = 2 + sin(x)
y = sin(x + 2)
y = 2 + cos(x)
4
Find the period of the given function.
5π
2π/5
π
2π
5
Which of the follow graphs is translated down 2, left π/2, and has a period of π?
y = -2 + sin(2x + π)
y = -2 sin(2x + π)
y = sin(2x + π/2) - 2
y = π/2 + sin(2x - 2)
6
Write a cosine function using the given information...
y = 3.5cos(π/4 x)
y = 8cos(3.5x)
y = 3.5cos(8x)
y = π/4cos(3.5x)
7
Given the equation, describe how the phase shift changed from the parent graph.
The graph shifted to the right by \frac{7\pi}{3}units.
The graph shifted to the left by \frac{7\pi}{3}units.
The graph shifted to the right by \frac{\pi}{3}units.
The graph shifted to the left by \frac{\pi}{3}units.
8
Find the translation of the cosine equation below.
Down 2
Left 2
Right π
Left π
9
Write an equation for the translation.
y = sin(x - 2)
y = sinx - 2
y = sinx + 2
y = sin(x + 2)
10
Which of the following equations matches the graph?
y = 2 sin (2x)
y = 2 sin(1/2 x)
y = 2 cos (1/4x)
y = 2 cos (4x)
11
Find the amplitude of the sine function
-5
5
2π/3
3
12
Find the period and amplitude of the cosine function
π, 8
π, 4
2π, 3
2π, 1
13
Determine the equation that has a period of π/2.
y = 2cos4x
y = 12sin(x-π)+4
y = -4sinx
y = -cos(x-40)
14
Which equation could match the graph?
y = 2 sin(2x)
y = -2 sin(2x)
y = 2 cos(2x)
y = -2 cos(2x)
15
Find the horizontal translation of the following function.
Right π/6
Left 3π/2
Right π/2
Left π/2
16
Describe any translations of the following function
Right 4, Up 3
Right 3, Up 4
Right 3, Down 4
Left 3, Up 4
17
Describe any translations in the cosine graph.
2 units right, 1 unit up
1 unit left, 2 units up
2 units right, 1 unit down
1 unit right, 2 units up
18
Which function has an amplitude of 2 and a period of π ?
f (x) = 2cos 2x
f (x) = (1/2)cos πx
f (x) = 2cos πx
f (x) =(1/2)cos 2x

13.7 Graphing Sine and Cosine Functions (translations) Flashcards | StudBud

13.7 Graphing Sine and Cosine Functions (translations)

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Period, amplitude, & phase shift of trigonometric functions. #trigonometry #mathematics #translations Pre-Calc Chapter 4 and Functions & trig 13.7

Flashcards18 cardsFPractice quizPHost liveL

Questions 18

Answers

1
Write a sine function that has amplitude 4, Period 4π, phase shift - 2, and vertical shift +1
y = 4sin1/2(x+2)+1
y = -4sin1/2(x-2)+1
y = 4sin4π(x+2)+1
y = 4cos1/2(x+2)+1
2
Write the equation for the graph, using a -sin function.
-sin(x-π)+3
3sinx
-sinx-3
-3sin(x-π)
3
Which equation could match the graph shown?
y = 2 cos (x)
y = 2 + sin(x)
y = sin(x + 2)
y = 2 + cos(x)
4
Find the period of the given function.
5π
2π/5
π
2π
5
Which of the follow graphs is translated down 2, left π/2, and has a period of π?
y = -2 + sin(2x + π)
y = -2 sin(2x + π)
y = sin(2x + π/2) - 2
y = π/2 + sin(2x - 2)
6
Write a cosine function using the given information...
y = 3.5cos(π/4 x)
y = 8cos(3.5x)
y = 3.5cos(8x)
y = π/4cos(3.5x)
7
Given the equation, describe how the phase shift changed from the parent graph.
The graph shifted to the right by \frac{7\pi}{3}units.
The graph shifted to the left by \frac{7\pi}{3}units.
The graph shifted to the right by \frac{\pi}{3}units.
The graph shifted to the left by \frac{\pi}{3}units.
8
Find the translation of the cosine equation below.
Down 2
Left 2
Right π
Left π
9
Write an equation for the translation.
y = sin(x - 2)
y = sinx - 2
y = sinx + 2
y = sin(x + 2)
10
Which of the following equations matches the graph?
y = 2 sin (2x)
y = 2 sin(1/2 x)
y = 2 cos (1/4x)
y = 2 cos (4x)
11
Find the amplitude of the sine function
-5
5
2π/3
3
12
Find the period and amplitude of the cosine function
π, 8
π, 4
2π, 3
2π, 1
13
Determine the equation that has a period of π/2.
y = 2cos4x
y = 12sin(x-π)+4
y = -4sinx
y = -cos(x-40)
14
Which equation could match the graph?
y = 2 sin(2x)
y = -2 sin(2x)
y = 2 cos(2x)
y = -2 cos(2x)
15
Find the horizontal translation of the following function.
Right π/6
Left 3π/2
Right π/2
Left π/2
16
Describe any translations of the following function
Right 4, Up 3
Right 3, Up 4
Right 3, Down 4
Left 3, Up 4
17
Describe any translations in the cosine graph.
2 units right, 1 unit up
1 unit left, 2 units up
2 units right, 1 unit down
1 unit right, 2 units up
18
Which function has an amplitude of 2 and a period of π ?
f (x) = 2cos 2x
f (x) = (1/2)cos πx
f (x) = 2cos πx
f (x) =(1/2)cos 2x