Let's now plot the graph of with in radians.
First, let's create a table for some of the values that we know:
Now, let's plot these points to estimate the graph of
If we inspect the unit circle carefully, we see that the function repeats itself every radians. Therefore, we can extend our plot using this periodicity property:
Some key characteristics of the graph of are as follows:
The domain of the function is almost except for the points where the function is undefined, namely
The range of the function is
The period of the function is
There is no minimum or maximum value.
The zeros occur at
The graph has vertical asymptotes at the points not in the domain: At each asymptote, the graph tends to from the left and from the right.
Which of the following plots is the graph of
Let's recall some of the basic properties of
The domain of the function is almost except for the points where the function is undefined, namely
The range of the function is
The period of the function is
There is no minimum or maximum value.
The zeros occur at
The graph has vertical asymptotes at the points not in the domain: At each asymptote, the graph tends to from the left and from the right.
Of the given plots, the only one that has all of these properties is III.
Which of the following plots is the graph of $y=\tan(x)?$
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a
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b
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c
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d
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e
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Which of the following plots is the graph of $y=\tan(x)?$
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a
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b
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c
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d
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e
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Which of the following -values is not in the domain of
Let's recall the graph of
The domain of the function contains all real numbers except for
Of the given values, the only one that is not in the domain is
Which of the following $x$-values is in the domain of $y=\tan x?$
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a
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$\dfrac{\pi}{2}$ |
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b
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$-\dfrac{\pi}{4}$ |
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c
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$\dfrac{-3\pi}{2}$ |
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d
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$\dfrac{3\pi}{2}$ |
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e
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$\dfrac{5\pi}{2}$ |
Which of the following is a zero of $y=\tan x?$
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a
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$x=\dfrac{3\pi}{2}$ |
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b
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$x=\pi$ |
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c
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$x=\dfrac{\pi}{2}$ |
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d
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$x=\dfrac{3\pi}{4}$ |
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e
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$x=\dfrac{5\pi}{4}$ |
The cotangent is the reciprocal of the tangent:
To plot the graph of with in radians, we create a table with some known values:
Plotting these points gives the following graph:
Notice that:
a zero on the graph of corresponds to a vertical asymptote on the graph of and
a vertical asymptote on the graph of corresponds to a zero on the graph of
The cotangent inherits its periodicity from the tangent, so the period of the cotangent is Using this periodicity property, we can extend our plot of the cotangent function:
Some key characteristics of the function are:
The domain is all real numbers except at the integer multiples of namely
The range of the function is
The period of the function is
There is no minimum or maximum value.
The zeros occur at
The graph has vertical asymptotes at the points that are not in the domain: and at each asymptote, the graph tends to from the left and from the right.
Which of the following plots is the graph of
Let's recall some of the basic properties of
The domain is all real numbers except at the integer multiples of :
The range of the function is
The period of the function is
There is no minimum or maximum value.
The zeros occur at
The graph has vertical asymptotes at the points that are not in the domain: and at each asymptote, the graph tends to from the left and from the right.
Of the given plots, the only one that has all of these properties is II.
Which of the following plots is the graph of $y=\cot x?$
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a
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b
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c
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d
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e
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Which of the following plots is the graph of $y=\cot x?$
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a
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b
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c
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d
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e
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Which of the following is the equation of a vertical asymptote of the function
Let's recall the graph of
The graph has vertical asymptotes at the points that are not in the domain:
At each asymptote, the graph tends to from the left and from the right.
Of the given equations, the only one that corresponds to an asymptote of the function is
Which of the following $x$-values is in the domain of $y = \cot x?$
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a
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$\pi$ |
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b
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$-5\pi$ |
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c
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$\dfrac{\pi}{2}$ |
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d
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$-4\pi$ |
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e
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$2\pi$ |
Which of the following is a zero of $y=\cot x?$
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a
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$x=\dfrac{3\pi}{4}$ |
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b
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$x=\dfrac{3\pi}{2}$ |
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c
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$x=\dfrac{2\pi}{3}$ |
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d
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$x=\dfrac{\pi}{3}$ |
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e
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$x=-\dfrac{\pi}{3}$ |
