Trigonometric Graphs (all six) - Pre-Calculus
Card 0 of 10
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 
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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 
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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 
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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 
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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
Thus, the function with a y-intercept of
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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 
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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 
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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 
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 
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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 
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