Trigonometric Graphs (all six) - Pre-Calculus
Card 0 of 40
Which of the trigonometric functions is represented by this graph?

Which of the trigonometric functions is represented by this graph?
This graph is the graph of y = csc x. The domain of this function is all real numbers except
where n is any integer. In other words, there are vertical asymptotes at all multiples of
. The range of this function is
. The period of this function is
.
This graph is the graph of y = csc x. The domain of this function is all real numbers except where n is any integer. In other words, there are vertical asymptotes at all multiples of
. The range of this function is
. The period of this function is
.
Compare your answer with the correct one above
Which of the following functions is represented by this graph?

Which of the following functions is represented by this graph?
This graph is the graph of y = cot x. The domain of this function is all real numbers except
where n is any integer. In other words, there are vertical asymptotes at all multiples of
. The range of this function is
. The period of this function is
.
This graph is the graph of y = cot x. The domain of this function is all real numbers except where n is any integer. In other words, there are vertical asymptotes at all multiples of
. The range of this function is
. The period of this function is
.
Compare your answer with the correct one above
Which of the following functions is represented by this graph?

Which of the following functions is represented by this graph?
This graph is the graph of y = sec x. The domain of this function is all real numbers except
where n is any integer. In other words, there are vertical asymptotes at
,
,
, and so on. The range of this function is
. The period of this function is 
This graph is the graph of y = sec x. The domain of this function is all real numbers except where n is any integer. In other words, there are vertical asymptotes at
,
,
, and so on. The range of this function is
. The period of this function is
Compare your answer with the correct one above
Which of the following functions is represented by this graph?

Which of the following functions is represented by this graph?
This graph is the graph of y = tan x. The domain of this function is all real numbers except
where n is any integer. In other words, there are vertical asymptotes at
, and so on. The range of this function is
. The period of this function is
.
This graph is the graph of y = tan x. The domain of this function is all real numbers except where n is any integer. In other words, there are vertical asymptotes at
, and so on. The range of this function is
. The period of this function is
.
Compare your answer with the correct one above
True or false: If you translate a sine curve 90o to the left along the x-axis, you will have a cosine curve.
True or false: If you translate a sine curve 90o to the left along the x-axis, you will have a cosine curve.
This is true! Notice the similarity of the shape between the graphs, but that they intercept the x-axis at different spots, and their peaks and valleys are at different spots.
y=sin(x), passes through the point (0,0)

y=cos(x), passes through the point (0,1)

This is true! Notice the similarity of the shape between the graphs, but that they intercept the x-axis at different spots, and their peaks and valleys are at different spots.
y=sin(x), passes through the point (0,0)
y=cos(x), passes through the point (0,1)
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Which of the following functions has a y-intercept of
?
Which of the following functions has a y-intercept of ?
The y-intercept of a function is found by substituting
. When we do this to each, we can determine the y-intercept. Don't forget your unit circle!





Thus, the function with a y-intercept of
is
.
The y-intercept of a function is found by substituting . When we do this to each, we can determine the y-intercept. Don't forget your unit circle!
Thus, the function with a y-intercept of is
.
Compare your answer with the correct one above
Which of the following functions is represented by this graph?

Which of the following functions is represented by this graph?
This graph is the graph of y = cos x. The domain of this function is all real numbers. The range of this function is
. The period of this function is
.
This graph is the graph of y = cos x. The domain of this function is all real numbers. The range of this function is . The period of this function is
.
Compare your answer with the correct one above
Which of the following functions is represented by this graph?

Which of the following functions is represented by this graph?
This graph is the graph of y = sin x. The domain of this function is all real numbers. The range of this function is
. The period of this function is
.
This graph is the graph of y = sin x. The domain of this function is all real numbers. The range of this function is . The period of this function is
.
Compare your answer with the correct one above
True or false: If you translate a secant function
units to the left along the x-axis, you will have a cosecant curve.
True or false: If you translate a secant function units to the left along the x-axis, you will have a cosecant curve.
This is false. While the graphs of secant and cosecant functions are related, in order to turn a secant function into a cosecant function, you'd need to translate the original graph
units to the right to obtain a cosecant graph.
This is false. While the graphs of secant and cosecant functions are related, in order to turn a secant function into a cosecant function, you'd need to translate the original graph units to the right to obtain a cosecant graph.
Compare your answer with the correct one above
Where does the tangent function intercept the x-axis?
Where does the tangent function intercept the x-axis?
Because the tangent function is periodic, it intercepts the x-axis in infinitely many places. We can see several of these in the graph below:

In the photo, we can see that the function is intercepting the x-axis at
Generalizing this, we can say that the tangent function intercepts the x-axis for
for all values of n such that n is an integer.
Because the tangent function is periodic, it intercepts the x-axis in infinitely many places. We can see several of these in the graph below:
In the photo, we can see that the function is intercepting the x-axis at Generalizing this, we can say that the tangent function intercepts the x-axis for
for all values of n such that n is an integer.
Compare your answer with the correct one above
True or false: If you translate a sine curve 90o to the left along the x-axis, you will have a cosine curve.
True or false: If you translate a sine curve 90o to the left along the x-axis, you will have a cosine curve.
This is true! Notice the similarity of the shape between the graphs, but that they intercept the x-axis at different spots, and their peaks and valleys are at different spots.
y=sin(x), passes through the point (0,0)

y=cos(x), passes through the point (0,1)

This is true! Notice the similarity of the shape between the graphs, but that they intercept the x-axis at different spots, and their peaks and valleys are at different spots.
y=sin(x), passes through the point (0,0)
y=cos(x), passes through the point (0,1)
Compare your answer with the correct one above
Which of the following functions is represented by this graph?

Which of the following functions is represented by this graph?
This graph is the graph of y = tan x. The domain of this function is all real numbers except
where n is any integer. In other words, there are vertical asymptotes at
, and so on. The range of this function is
. The period of this function is
.
This graph is the graph of y = tan x. The domain of this function is all real numbers except where n is any integer. In other words, there are vertical asymptotes at
, and so on. The range of this function is
. The period of this function is
.
Compare your answer with the correct one above
Which of the trigonometric functions is represented by this graph?

Which of the trigonometric functions is represented by this graph?
This graph is the graph of y = csc x. The domain of this function is all real numbers except
where n is any integer. In other words, there are vertical asymptotes at all multiples of
. The range of this function is
. The period of this function is
.
This graph is the graph of y = csc x. The domain of this function is all real numbers except where n is any integer. In other words, there are vertical asymptotes at all multiples of
. The range of this function is
. The period of this function is
.
Compare your answer with the correct one above
Which of the following functions is represented by this graph?

Which of the following functions is represented by this graph?
This graph is the graph of y = cot x. The domain of this function is all real numbers except
where n is any integer. In other words, there are vertical asymptotes at all multiples of
. The range of this function is
. The period of this function is
.
This graph is the graph of y = cot x. The domain of this function is all real numbers except where n is any integer. In other words, there are vertical asymptotes at all multiples of
. The range of this function is
. The period of this function is
.
Compare your answer with the correct one above
Which of the following functions is represented by this graph?

Which of the following functions is represented by this graph?
This graph is the graph of y = sec x. The domain of this function is all real numbers except
where n is any integer. In other words, there are vertical asymptotes at
,
,
, and so on. The range of this function is
. The period of this function is 
This graph is the graph of y = sec x. The domain of this function is all real numbers except where n is any integer. In other words, there are vertical asymptotes at
,
,
, and so on. The range of this function is
. The period of this function is
Compare your answer with the correct one above
Which of the following functions has a y-intercept of
?
Which of the following functions has a y-intercept of ?
The y-intercept of a function is found by substituting
. When we do this to each, we can determine the y-intercept. Don't forget your unit circle!





Thus, the function with a y-intercept of
is
.
The y-intercept of a function is found by substituting . When we do this to each, we can determine the y-intercept. Don't forget your unit circle!
Thus, the function with a y-intercept of is
.
Compare your answer with the correct one above
Which of the following functions is represented by this graph?

Which of the following functions is represented by this graph?
This graph is the graph of y = cos x. The domain of this function is all real numbers. The range of this function is
. The period of this function is
.
This graph is the graph of y = cos x. The domain of this function is all real numbers. The range of this function is . The period of this function is
.
Compare your answer with the correct one above
Which of the following functions is represented by this graph?

Which of the following functions is represented by this graph?
This graph is the graph of y = sin x. The domain of this function is all real numbers. The range of this function is
. The period of this function is
.
This graph is the graph of y = sin x. The domain of this function is all real numbers. The range of this function is . The period of this function is
.
Compare your answer with the correct one above
True or false: If you translate a secant function
units to the left along the x-axis, you will have a cosecant curve.
True or false: If you translate a secant function units to the left along the x-axis, you will have a cosecant curve.
This is false. While the graphs of secant and cosecant functions are related, in order to turn a secant function into a cosecant function, you'd need to translate the original graph
units to the right to obtain a cosecant graph.
This is false. While the graphs of secant and cosecant functions are related, in order to turn a secant function into a cosecant function, you'd need to translate the original graph units to the right to obtain a cosecant graph.
Compare your answer with the correct one above
Where does the tangent function intercept the x-axis?
Where does the tangent function intercept the x-axis?
Because the tangent function is periodic, it intercepts the x-axis in infinitely many places. We can see several of these in the graph below:

In the photo, we can see that the function is intercepting the x-axis at
Generalizing this, we can say that the tangent function intercepts the x-axis for
for all values of n such that n is an integer.
Because the tangent function is periodic, it intercepts the x-axis in infinitely many places. We can see several of these in the graph below:
In the photo, we can see that the function is intercepting the x-axis at Generalizing this, we can say that the tangent function intercepts the x-axis for
for all values of n such that n is an integer.
Compare your answer with the correct one above