S2w1 FC Graphing and inverting trig functions

Last updated 8 months ago

31 questions

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S2w1 FC Graphing and inverting trig functions

Last updated 8 months ago

31 questions

1

Required

1

watch the following video on graphing trig fuctions. Do you have any questions?

Required

1

Required

1

watch the following animation showing the connection between a wheel turning and two different sinusoidal waves being drawn. pay attention to where the sine wave is when the point is at its highest, notice what part of the graph is shown after one revolution.
What do you notice?

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About how long would you say you have worked on this formative so far? Note that there are two very different sections of this homework - graphing and inversing. It may be helpful to spend some time doing homework questions (roughly the first half of the assignment) or work of practicing using your module. Come back to the second half later.

1

Ok, have you rested your working memory?

1

Draggable item		Corresponding Item

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What is the relationship between the domain and range of the exponential parent function and the logarithmic parent function?

1

What is the domain of the sinusoidal function cos(x)?

1

What is the range of the sinusoidal function cos(x)?

1

what do you think the domain of the inverse of sine (written as arcsine, also sin^-1) should be?

1

y=x^2 is not a one to one function, but we have a sortof inverse for that function anyway - what do we do to "undo" the squaring function.

1

looking at the unit circle above: what is

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Why can the answer above definately not be

Required

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Review: if y=f(x), and g(x)=4f(x), what transformation takes place?

translation up or down

translation side to side

dilation up and down

dilation side to side

Review: if y=f(x), and g(x)=f(4x), what transformation takes place?

translation up or down

translation side to side

dilation up and down

dilation side to side

watch the following video on graphing trig fuctions. Do you have any questions?

according to the video, what does the amplitude of a sine function refer to?

the amount of the translation up or down

the amount of the translation side to side

the amount of the dilation up and down

the amount of the dilation side to side

the line of equilibrium is frequently at 0. When it is not at zero, what function transformation must have happened?

translation up or down

translation side to side

dilation up and down

dilation side to side

watch the following animation showing the connection between a wheel turning and two different sinusoidal waves being drawn. pay attention to where the sine wave is when the point is at its highest, notice what part of the graph is shown after one revolution.
What do you notice?

Consider a graph where the x-axis signifies the degree, and the graph is showing the y-component of a spot on a wheel as the wheel is turning. The dot starts at (0,1) if you were to plot the same dot, but instead of using theta as the x axis, you are using time as the x axis, where do you think the graph would hit the x axis?

at 2π

after 1 minute

when the wheel had made a complete rotation

when the wheel had made a quarter rotation

If you want to talk about how fast a wheel is moving, what units do you use?

miles per hour

meter/second

revolutions/seconds

seconds

if a wheel is moving at 1 revolution per second, how many degrees has that wheel moved in 0.5 seconds?

45°

90°

135°

180°

sin and cosine are functions that take angle measurement as inputs. Cos(t) where the units of t are seconds doesn't make a lot of sense. So consider cos(g(t)) if g(x) =2t, where 2 is the rate of speed of the wheel and has the units revolutions/sec, what is the unit of g(x)?

degrees

radians

revolutions

seconds

About how long would you say you have worked on this formative so far? Note that there are two very different sections of this homework - graphing and inversing. It may be helpful to spend some time doing homework questions (roughly the first half of the assignment) or work of practicing using your module. Come back to the second half later.

Ok, have you rested your working memory?

Match degrees to the appropriate unit circle radian measure.

Draggable item		Corresponding Item
60		0
120
45
30
135
270
315
300
210
360
0

What is the relationship between the domain and range of the exponential parent function and the logarithmic parent function?

What is the domain of the sinusoidal function cos(x)?

What is the range of the sinusoidal function cos(x)?

what do you think the domain of the inverse of sine (written as arcsine, also sin^-1) should be?

y=x^2 is not a one to one function, but we have a sortof inverse for that function anyway - what do we do to "undo" the squaring function.

Find the measure of the indicated angle (?) round to the nearest tenth, use a calculator.

9.4

20.15

55.2

19.4

Solve for the missing angle

32°

61°

44°

50°

looking at the unit circle above: what is

Why can the answer above definately not be

Categorize the different parts of the lesson.

how to transform sinusoidal functions
what the amplitude of a sine wave is
what the period of a sine wave is
how to graph sine waves
What the equilibrium line of a function represents
how to have a rate of change as part of the function inside a sin function
the relationship of
to arcsin x
the lack of relationship of
to
how to deal with tan, cot, sec and csc by just turning them into sin and cos
the domain and range of an inverse trig function
how to graph the tan, cot, sec and csc functions
finding sides of right triangles given a side and an angle
finding the angle of a right triangle given two sides

Im good
im fuzzy
so confused

Review: if y=f(x), and g(x)=4f(x), what transformation takes place?

translation up or down

translation side to side

dilation up and down

dilation side to side

Review: if y=f(x), and g(x)=f(4x), what transformation takes place?

translation up or down

translation side to side

dilation up and down

dilation side to side

according to the video, what does the amplitude of a sine function refer to?

the amount of the translation up or down

the amount of the translation side to side

the amount of the dilation up and down

the amount of the dilation side to side

the line of equilibrium is frequently at 0. When it is not at zero, what function transformation must have happened?

translation up or down

translation side to side

dilation up and down

dilation side to side

Consider a graph where the x-axis signifies the degree, and the graph is showing the y-component of a spot on a wheel as the wheel is turning. The dot starts at (0,1)

if you were to plot the same dot, but instead of using theta as the x axis, you are using time as the x axis, where do you think the graph would hit the x axis?

at 2π

after 1 minute

when the wheel had made a complete rotation

when the wheel had made a quarter rotation

If you want to talk about how fast a wheel is moving, what units do you use?

miles per hour

meter/second

revolutions/seconds

seconds

if a wheel is moving at 1 revolution per second, how many degrees has that wheel moved in 0.5 seconds?

45°

90°

135°

180°

sin and cosine are functions that take angle measurement as inputs. Cos(t) where the units of t are seconds doesn't make a lot of sense. So consider cos(g(t))  if g(x) =2t, where 2 is the rate of speed of the wheel and has the units revolutions/sec, what is the unit of g(x)?

degrees

radians

revolutions

seconds

Match degrees to the appropriate unit circle radian measure.

Which of the following describes the set of ordered pairs?

Function

One-to-one Function

Neither

Which of the following describes the set of ordered pairs?

Function

One-to-one Function

Neither

Which of the following describes the relation shown?

Function

One-to-one Function

Neither

Which of the following describes the relation?

Function

One-to-one Function

Neither

Which of the following describes the graph?

Function

One-to-one Function

Neither

Which of the following describes the graph?

Function

One-to-one Function

Neither

g is the inverse of f.

True

False

g is the inverse of f.

True

False

Find the measure of the indicated angle (?) round to the nearest tenth, use a calculator.

9.4

20.15

55.2

19.4

Solve for the missing angle

32°

61°

44°

50°

Categorize the different parts of the lesson. 

how to transform sinusoidal functions

what the amplitude of a sine wave is

what the period of a sine wave is

how to graph sine waves

What the equilibrium line of a function represents

how to have a rate of change as part of the function inside a sin function

the relationship of 
to arcsin x

the lack of relationship of 
 to

how to deal with tan, cot, sec and csc by just turning them into sin and cos

the domain and range of an inverse trig function

how to graph the tan, cot, sec and csc functions

finding sides of right triangles given a side and an angle

finding the angle of a right triangle given two sides

Im good

im fuzzy

so confused

Which of the following describes the set of ordered pairs? 

Function

One-to-one Function

Neither

Which of the following describes the set of ordered pairs?

Function

One-to-one Function

Neither

Which of the following describes the relation shown?

Function

One-to-one Function

Neither

Which of the following describes the relation?

Function

One-to-one Function

Neither

Which of the following describes the graph?

Function

One-to-one Function

Neither

Which of the following describes the graph?

Function

One-to-one Function

Neither

g is the inverse of f.

True

False

g is the inverse of f.

True

False

S2w1 FC Graphing and inverting trig functions

S2w1 FC Graphing and inverting trig functions

watch the following video on graphing trig fuctions. Do you have any questions?

watch the following animation showing the connection between a wheel turning and two different sinusoidal waves being drawn. pay attention to where the sine wave is when the point is at its highest, notice what part of the graph is shown after one revolution.What do you notice?

Ok, have you rested your working memory?

What is the relationship between the domain and range of the exponential parent function and the logarithmic parent function?

What is the domain of the sinusoidal function cos(x)?

What is the range of the sinusoidal function cos(x)?

what do you think the domain of the inverse of sine (written as arcsine, also sin^-1) should be?

y=x^2 is not a one to one function, but we have a sortof inverse for that function anyway - what do we do to "undo" the squaring function.

looking at the unit circle above: what is

Why can the answer above definately not be

Review: if y=f(x), and g(x)=4f(x), what transformation takes place?

Review: if y=f(x), and g(x)=f(4x), what transformation takes place?

watch the following video on graphing trig fuctions. Do you have any questions?

according to the video, what does the amplitude of a sine function refer to?

the line of equilibrium is frequently at 0. When it is not at zero, what function transformation must have happened?

watch the following animation showing the connection between a wheel turning and two different sinusoidal waves being drawn. pay attention to where the sine wave is when the point is at its highest, notice what part of the graph is shown after one revolution.What do you notice?

If you want to talk about how fast a wheel is moving, what units do you use?

if a wheel is moving at 1 revolution per second, how many degrees has that wheel moved in 0.5 seconds?

sin and cosine are functions that take angle measurement as inputs. Cos(t) where the units of t are seconds doesn't make a lot of sense. So consider cos(g(t)) if g(x) =2t, where 2 is the rate of speed of the wheel and has the units revolutions/sec, what is the unit of g(x)?

Ok, have you rested your working memory?

Match degrees to the appropriate unit circle radian measure.

What is the relationship between the domain and range of the exponential parent function and the logarithmic parent function?

What is the domain of the sinusoidal function cos(x)?

What is the range of the sinusoidal function cos(x)?

what do you think the domain of the inverse of sine (written as arcsine, also sin^-1) should be?

y=x^2 is not a one to one function, but we have a sortof inverse for that function anyway - what do we do to "undo" the squaring function.

Find the measure of the indicated angle (?) round to the nearest tenth, use a calculator.

Solve for the missing angle

looking at the unit circle above: what is

Why can the answer above definately not be

Categorize the different parts of the lesson.

Which of the following describes the set of ordered pairs?

Which of the following describes the set of ordered pairs?

Which of the following describes the relation shown?

Which of the following describes the relation?

Which of the following describes the graph?

Which of the following describes the graph?

g is the inverse of f.

g is the inverse of f.

watch the following animation showing the connection between a wheel turning and two different sinusoidal waves being drawn. pay attention to where the sine wave is when the point is at its highest, notice what part of the graph is shown after one revolution.
What do you notice?

watch the following animation showing the connection between a wheel turning and two different sinusoidal waves being drawn. pay attention to where the sine wave is when the point is at its highest, notice what part of the graph is shown after one revolution.
What do you notice?