Graphs of Trig Functions
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There is not a whole lot to this section. It is here just to remind you of the graphs
of the six trig functions as well as a couple of nice properties about trig
functions.
Before jumping into the problems remember we saw in the Trig Function Evaluation section that trig
functions are examples of periodic
functions. This means that all we really
need to do is graph the function for one periods length of values then repeat
the graph.
Graph the following function.
1.
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There really isn’t a whole lot to
this one other than plotting a few points between 0 and ,
then repeat. Remember cosine has a
period of (see Problem 6 in Trig
Function Evaluation).
Here’s the graph for .
Notice that graph does repeat
itself 4 times in this range of x’s
as it should.
Let’s also note here that we can
put all values of x into cosine
(which won’t be the case for most of the trig functions) and let’s also note
that
It is important to notice that
cosine will never be larger than 1 or smaller than -1. This will be useful on occasion in a calculus
class.
2.
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3.
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In this case I added a 5 in front
of the cosine. All that this will do is
increase how big cosine will get. The
number in front of the cosine or sine is called the amplitude. Here’s the graph
of this function.
Note the scale on the y-axis for this problem and do not
confuse it with the previous graph. The y-axis scales are different!
In general,
4.
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As with the first problem in this
section there really isn’t a lot to do other than graph it. Here is the graph on the range .
From this graph we can see that
sine has the same range that cosine does.
In general
As with cosine, sine itself will
never be larger than 1 and never smaller than -1.
5.
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6.
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7.
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8.
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For this graph we will have to
avoid x’s where sine is zero . So, the graph of cosecant will not exist for
Here is the graph of cosecant.
Cosecant will have the same range
as secant.
9.
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Cotangent must avoid
since we will have division by
zero at these points. Here is the graph.
Cotangent has the following range.